Algebra Examples

$(- x^{5} y^{5} - \frac{1}{4} x^{3} y^{2} + \frac{2}{3} x^{5} y - 6 x y^{3}) \div (- 3 x^{2} y^{3})$

Step 1

Rewrite the division as a fraction.

$\frac{- x^{5} y^{5} - \frac{1}{4} \cdot (x^{3} y^{2}) + \frac{2}{3} \cdot (x^{5} y) - 6 x y^{3}}{- 3 x^{2} y^{3}}$

Step 2

Simplify the numerator.

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Step 2.1

Factor

$x y$ out of

$- x^{5} y^{5} - \frac{1}{4} \cdot x^{3} y^{2} + \frac{2}{3} \cdot x^{5} y - 6 x y^{3}$ .

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Step 2.1.1

Factor

$x y$ out of

$- x^{5} y^{5}$ .

$\frac{x y (- x^{4} y^{4}) - \frac{1}{4} \cdot x^{3} y^{2} + \frac{2}{3} \cdot x^{5} y - 6 x y^{3}}{- 3 x^{2} y^{3}}$

Step 2.1.2

Factor

$x y$ out of

$- \frac{1}{4} \cdot x^{3} y^{2}$ .

$\frac{x y (- x^{4} y^{4}) + x y (- \frac{1}{4} \cdot x^{2} y) + \frac{2}{3} \cdot x^{5} y - 6 x y^{3}}{- 3 x^{2} y^{3}}$

Step 2.1.3

Factor

$x y$ out of

$\frac{2}{3} \cdot x^{5} y$ .

$\frac{x y (- x^{4} y^{4}) + x y (- \frac{1}{4} \cdot x^{2} y) + x y (\frac{2}{3} \cdot x^{4}) - 6 x y^{3}}{- 3 x^{2} y^{3}}$

Step 2.1.4

Factor

$x y$ out of

$- 6 x y^{3}$ .

$\frac{x y (- x^{4} y^{4}) + x y (- \frac{1}{4} \cdot x^{2} y) + x y (\frac{2}{3} \cdot x^{4}) + x y (- 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.1.5

Factor

$x y$ out of

$x y (- x^{4} y^{4}) + x y (- \frac{1}{4} \cdot x^{2} y)$ .

$\frac{x y (- x^{4} y^{4} - \frac{1}{4} \cdot x^{2} y) + x y (\frac{2}{3} \cdot x^{4}) + x y (- 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.1.6

Factor

$x y$ out of

$x y (- x^{4} y^{4} - \frac{1}{4} \cdot x^{2} y) + x y (\frac{2}{3} \cdot x^{4})$ .

$\frac{x y (- x^{4} y^{4} - \frac{1}{4} \cdot x^{2} y + \frac{2}{3} \cdot x^{4}) + x y (- 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.1.7

Factor

$x y$ out of

$x y (- x^{4} y^{4} - \frac{1}{4} \cdot x^{2} y + \frac{2}{3} \cdot x^{4}) + x y (- 6 y^{2})$ .

$\frac{x y (- x^{4} y^{4} - \frac{1}{4} \cdot x^{2} y + \frac{2}{3} \cdot x^{4} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.2

Combine exponents.

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Step 2.2.1

Combine

$x^{2}$ and

$\frac{1}{4}$ .

$\frac{x y (- x^{4} y^{4} - \frac{x^{2}}{4} y + \frac{2}{3} \cdot x^{4} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.2.2

Combine

$y$ and

$\frac{x^{2}}{4}$ .

$\frac{x y (- x^{4} y^{4} - \frac{y x^{2}}{4} + \frac{2}{3} \cdot x^{4} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.2.3

Combine

$\frac{2}{3}$ and

$x^{4}$ .

$\frac{x y (- x^{4} y^{4} - \frac{y x^{2}}{4} + \frac{2 x^{4}}{3} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.3

To write

$- x^{4} y^{4}$ as a fraction with a common denominator, multiply by

$\frac{4}{4}$ .

$\frac{x y (- x^{4} y^{4} \cdot \frac{4}{4} - \frac{y x^{2}}{4} + \frac{2 x^{4}}{3} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.4

Combine

$- x^{4} y^{4}$ and

$\frac{4}{4}$ .

$\frac{x y (\frac{- x^{4} y^{4} \cdot 4}{4} - \frac{y x^{2}}{4} + \frac{2 x^{4}}{3} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.5

Combine the numerators over the common denominator.

$\frac{x y (\frac{- x^{4} y^{4} \cdot 4 - y x^{2}}{4} + \frac{2 x^{4}}{3} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.6

Simplify the numerator.

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Step 2.6.1

Factor

$x^{2} y$ out of

$- x^{4} y^{4} \cdot 4 - y x^{2}$ .

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Step 2.6.1.1

Factor

$x^{2} y$ out of

$- x^{4} y^{4} \cdot 4$ .

$\frac{x y (\frac{x^{2} y (- x^{2} y^{3} \cdot 4) - y x^{2}}{4} + \frac{2 x^{4}}{3} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.6.1.2

Factor

$x^{2} y$ out of

$- y x^{2}$ .

$\frac{x y (\frac{x^{2} y (- x^{2} y^{3} \cdot 4) + x^{2} y (- 1)}{4} + \frac{2 x^{4}}{3} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.6.1.3

Factor

$x^{2} y$ out of

$x^{2} y (- x^{2} y^{3} \cdot 4) + x^{2} y (- 1)$ .

$\frac{x y (\frac{x^{2} y (- x^{2} y^{3} \cdot 4 - 1)}{4} + \frac{2 x^{4}}{3} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.6.2

Multiply

$4$ by

$- 1$ .

$\frac{x y (\frac{x^{2} y (- 4 x^{2} y^{3} - 1)}{4} + \frac{2 x^{4}}{3} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.7

To write

$\frac{x^{2} y (- 4 x^{2} y^{3} - 1)}{4}$ as a fraction with a common denominator, multiply by

$\frac{3}{3}$ .

$\frac{x y (\frac{x^{2} y (- 4 x^{2} y^{3} - 1)}{4} \cdot \frac{3}{3} + \frac{2 x^{4}}{3} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.8

To write

$\frac{2 x^{4}}{3}$ as a fraction with a common denominator, multiply by

$\frac{4}{4}$ .

$\frac{x y (\frac{x^{2} y (- 4 x^{2} y^{3} - 1)}{4} \cdot \frac{3}{3} + \frac{2 x^{4}}{3} \cdot \frac{4}{4} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.9

Write each expression with a common denominator of

$12$ , by multiplying each by an appropriate factor of

$1$ .

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Step 2.9.1

Multiply

$\frac{x^{2} y (- 4 x^{2} y^{3} - 1)}{4}$ by

$\frac{3}{3}$ .

$\frac{x y (\frac{x^{2} y (- 4 x^{2} y^{3} - 1) \cdot 3}{4 \cdot 3} + \frac{2 x^{4}}{3} \cdot \frac{4}{4} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.9.2

Multiply

$4$ by

$3$ .

$\frac{x y (\frac{x^{2} y (- 4 x^{2} y^{3} - 1) \cdot 3}{12} + \frac{2 x^{4}}{3} \cdot \frac{4}{4} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.9.3

Multiply

$\frac{2 x^{4}}{3}$ by

$\frac{4}{4}$ .

$\frac{x y (\frac{x^{2} y (- 4 x^{2} y^{3} - 1) \cdot 3}{12} + \frac{2 x^{4} \cdot 4}{3 \cdot 4} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.9.4

Multiply

$3$ by

$4$ .

$\frac{x y (\frac{x^{2} y (- 4 x^{2} y^{3} - 1) \cdot 3}{12} + \frac{2 x^{4} \cdot 4}{12} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.10

Combine the numerators over the common denominator.

$\frac{x y (\frac{x^{2} y (- 4 x^{2} y^{3} - 1) \cdot 3 + 2 x^{4} \cdot 4}{12} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.11

Simplify the numerator.

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Step 2.11.1

Factor

$x^{2}$ out of

$x^{2} y (- 4 x^{2} y^{3} - 1) \cdot 3 + 2 x^{4} \cdot 4$ .

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Step 2.11.1.1

Factor

$x^{2}$ out of

$x^{2} y (- 4 x^{2} y^{3} - 1) \cdot 3$ .

$\frac{x y (\frac{x^{2} ((y (- 4 x^{2} y^{3} - 1)) \cdot 3) + 2 x^{4} \cdot 4}{12} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.11.1.2

Factor

$x^{2}$ out of

$2 x^{4} \cdot 4$ .

$\frac{x y (\frac{x^{2} ((y (- 4 x^{2} y^{3} - 1)) \cdot 3) + x^{2} (2 x^{2} \cdot 4)}{12} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.11.1.3

Factor

$x^{2}$ out of

$x^{2} ((y (- 4 x^{2} y^{3} - 1)) \cdot 3) + x^{2} (2 x^{2} \cdot 4)$ .

$\frac{x y (\frac{x^{2} ((y (- 4 x^{2} y^{3} - 1)) \cdot 3 + 2 x^{2} \cdot 4)}{12} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.11.2

Apply the distributive property.

$\frac{x y (\frac{x^{2} ((y (- 4 x^{2} y^{3}) + y \cdot - 1) \cdot 3 + 2 x^{2} \cdot 4)}{12} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.11.3

Rewrite using the commutative property of multiplication.

$\frac{x y (\frac{x^{2} ((- 4 y (x^{2} y^{3}) + y \cdot - 1) \cdot 3 + 2 x^{2} \cdot 4)}{12} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.11.4

Move

$- 1$ to the left of

$y$ .

$\frac{x y (\frac{x^{2} ((- 4 y (x^{2} y^{3}) - 1 \cdot y) \cdot 3 + 2 x^{2} \cdot 4)}{12} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.11.5

Simplify each term.

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Step 2.11.5.1

Multiply

$y$ by

$y^{3}$ by adding the exponents.

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Step 2.11.5.1.1

Move

$y^{3}$ .

$\frac{x y (\frac{x^{2} ((- 4 (y^{3} y) x^{2} - 1 \cdot y) \cdot 3 + 2 x^{2} \cdot 4)}{12} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.11.5.1.2

Multiply

$y^{3}$ by

$y$ .

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Step 2.11.5.1.2.1

Raise

$y$ to the power of

$1$ .

$\frac{x y (\frac{x^{2} ((- 4 (y^{3} y^{1}) x^{2} - 1 \cdot y) \cdot 3 + 2 x^{2} \cdot 4)}{12} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.11.5.1.2.2

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{x y (\frac{x^{2} ((- 4 y^{3 + 1} x^{2} - 1 \cdot y) \cdot 3 + 2 x^{2} \cdot 4)}{12} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.11.5.1.3

Add

$3$ and

$1$ .

$\frac{x y (\frac{x^{2} ((- 4 y^{4} x^{2} - 1 \cdot y) \cdot 3 + 2 x^{2} \cdot 4)}{12} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.11.5.2

Rewrite

$- 1 y$ as

$- y$ .

$\frac{x y (\frac{x^{2} ((- 4 y^{4} x^{2} - y) \cdot 3 + 2 x^{2} \cdot 4)}{12} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.11.6

Apply the distributive property.

$\frac{x y (\frac{x^{2} (- 4 y^{4} x^{2} \cdot 3 - y \cdot 3 + 2 x^{2} \cdot 4)}{12} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.11.7

Multiply

$3$ by

$- 4$ .

$\frac{x y (\frac{x^{2} (- 12 y^{4} x^{2} - y \cdot 3 + 2 x^{2} \cdot 4)}{12} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.11.8

Multiply

$3$ by

$- 1$ .

$\frac{x y (\frac{x^{2} (- 12 y^{4} x^{2} - 3 y + 2 x^{2} \cdot 4)}{12} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.11.9

Multiply

$4$ by

$2$ .

$\frac{x y (\frac{x^{2} (- 12 y^{4} x^{2} - 3 y + 8 x^{2})}{12} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.12

To write

$- 6 y^{2}$ as a fraction with a common denominator, multiply by

$\frac{12}{12}$ .

$\frac{x y (\frac{x^{2} (- 12 y^{4} x^{2} - 3 y + 8 x^{2})}{12} - 6 y^{2} \cdot \frac{12}{12})}{- 3 x^{2} y^{3}}$

Step 2.13

Combine

$- 6 y^{2}$ and

$\frac{12}{12}$ .

$\frac{x y (\frac{x^{2} (- 12 y^{4} x^{2} - 3 y + 8 x^{2})}{12} + \frac{- 6 y^{2} \cdot 12}{12})}{- 3 x^{2} y^{3}}$

Step 2.14

Combine the numerators over the common denominator.

$\frac{x y \frac{x^{2} (- 12 y^{4} x^{2} - 3 y + 8 x^{2}) - 6 y^{2} \cdot 12}{12}}{- 3 x^{2} y^{3}}$

Step 2.15

Simplify the numerator.

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Step 2.15.1

Apply the distributive property.

$\frac{x y \frac{x^{2} (- 12 y^{4} x^{2}) + x^{2} (- 3 y) + x^{2} (8 x^{2}) - 6 y^{2} \cdot 12}{12}}{- 3 x^{2} y^{3}}$

Step 2.15.2

Simplify.

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Step 2.15.2.1

Rewrite using the commutative property of multiplication.

$\frac{x y \frac{- 12 x^{2} (y^{4} x^{2}) + x^{2} (- 3 y) + x^{2} (8 x^{2}) - 6 y^{2} \cdot 12}{12}}{- 3 x^{2} y^{3}}$

Step 2.15.2.2

Rewrite using the commutative property of multiplication.

$\frac{x y \frac{- 12 x^{2} (y^{4} x^{2}) - 3 x^{2} y + x^{2} (8 x^{2}) - 6 y^{2} \cdot 12}{12}}{- 3 x^{2} y^{3}}$

Step 2.15.2.3

Rewrite using the commutative property of multiplication.

$\frac{x y \frac{- 12 x^{2} (y^{4} x^{2}) - 3 x^{2} y + 8 x^{2} x^{2} - 6 y^{2} \cdot 12}{12}}{- 3 x^{2} y^{3}}$

Step 2.15.3

Simplify each term.

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Step 2.15.3.1

Multiply

$x^{2}$ by

$x^{2}$ by adding the exponents.

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Step 2.15.3.1.1

Move

$x^{2}$ .

$\frac{x y \frac{- 12 (x^{2} x^{2}) y^{4} - 3 x^{2} y + 8 x^{2} x^{2} - 6 y^{2} \cdot 12}{12}}{- 3 x^{2} y^{3}}$

Step 2.15.3.1.2

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{x y \frac{- 12 x^{2 + 2} y^{4} - 3 x^{2} y + 8 x^{2} x^{2} - 6 y^{2} \cdot 12}{12}}{- 3 x^{2} y^{3}}$

Step 2.15.3.1.3

Add

$2$ and

$2$ .

$\frac{x y \frac{- 12 x^{4} y^{4} - 3 x^{2} y + 8 x^{2} x^{2} - 6 y^{2} \cdot 12}{12}}{- 3 x^{2} y^{3}}$

Step 2.15.3.2

Multiply

$x^{2}$ by

$x^{2}$ by adding the exponents.

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Step 2.15.3.2.1

Move

$x^{2}$ .

$\frac{x y \frac{- 12 x^{4} y^{4} - 3 x^{2} y + 8 (x^{2} x^{2}) - 6 y^{2} \cdot 12}{12}}{- 3 x^{2} y^{3}}$

Step 2.15.3.2.2

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{x y \frac{- 12 x^{4} y^{4} - 3 x^{2} y + 8 x^{2 + 2} - 6 y^{2} \cdot 12}{12}}{- 3 x^{2} y^{3}}$

Step 2.15.3.2.3

Add

$2$ and

$2$ .

$\frac{x y \frac{- 12 x^{4} y^{4} - 3 x^{2} y + 8 x^{4} - 6 y^{2} \cdot 12}{12}}{- 3 x^{2} y^{3}}$

Step 2.15.4

Multiply

$12$ by

$- 6$ .

$\frac{x y \frac{- 12 x^{4} y^{4} - 3 x^{2} y + 8 x^{4} - 72 y^{2}}{12}}{- 3 x^{2} y^{3}}$

Step 2.16

Combine exponents.

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Step 2.16.1

Combine

$x$ and

$\frac{- 12 x^{4} y^{4} - 3 x^{2} y + 8 x^{4} - 72 y^{2}}{12}$ .

$\frac{y \frac{x (- 12 x^{4} y^{4} - 3 x^{2} y + 8 x^{4} - 72 y^{2})}{12}}{- 3 x^{2} y^{3}}$

Step 2.16.2

Combine

$y$ and

$\frac{x (- 12 x^{4} y^{4} - 3 x^{2} y + 8 x^{4} - 72 y^{2})}{12}$ .

$\frac{\frac{y (x (- 12 x^{4} y^{4} - 3 x^{2} y + 8 x^{4} - 72 y^{2}))}{12}}{- 3 x^{2} y^{3}}$

Step 2.17

Remove unnecessary parentheses.

$\frac{\frac{y x (- 12 x^{4} y^{4} - 3 x^{2} y + 8 x^{4} - 72 y^{2})}{12}}{- 3 x^{2} y^{3}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{y x (- 12 x^{4} y^{4} - 3 x^{2} y + 8 x^{4} - 72 y^{2})}{12} \cdot \frac{1}{- 3 x^{2} y^{3}}$

Step 4

Combine.

$\frac{y x (- 12 x^{4} y^{4} - 3 x^{2} y + 8 x^{4} - 72 y^{2}) \cdot 1}{12 (- 3 x^{2} y^{3})}$

Step 5

Cancel the common factor of

$y$ and

$y^{3}$ .

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Step 5.1

Factor

$y$ out of

$y x (- 12 x^{4} y^{4} - 3 x^{2} y + 8 x^{4} - 72 y^{2}) \cdot 1$ .

$\frac{y ((x (- 12 x^{4} y^{4} - 3 x^{2} y + 8 x^{4} - 72 y^{2})) \cdot 1)}{12 (- 3 x^{2} y^{3})}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor

$y$ out of

$12 (- 3 x^{2} y^{3})$ .

$\frac{y ((x (- 12 x^{4} y^{4} - 3 x^{2} y + 8 x^{4} - 72 y^{2})) \cdot 1)}{y (12 (- 3 x^{2} y^{2}))}$

Step 5.2.2

Cancel the common factor.

$\frac{y ((x (- 12 x^{4} y^{4} - 3 x^{2} y + 8 x^{4} - 72 y^{2})) \cdot 1)}{y (12 (- 3 x^{2} y^{2}))}$

Step 5.2.3

Rewrite the expression.

$\frac{(x (- 12 x^{4} y^{4} - 3 x^{2} y + 8 x^{4} - 72 y^{2})) \cdot 1}{12 (- 3 x^{2} y^{2})}$

Step 6

Cancel the common factor of

$x$ and

$x^{2}$ .

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Step 6.1

Factor

$x$ out of

$(x (- 12 x^{4} y^{4} - 3 x^{2} y + 8 x^{4} - 72 y^{2})) \cdot 1$ .

$\frac{x ((- 12 x^{4} y^{4} - 3 x^{2} y + 8 x^{4} - 72 y^{2}) \cdot 1)}{12 (- 3 x^{2} y^{2})}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor

$x$ out of

$12 (- 3 x^{2} y^{2})$ .

$\frac{x ((- 12 x^{4} y^{4} - 3 x^{2} y + 8 x^{4} - 72 y^{2}) \cdot 1)}{x (12 (- 3 x y^{2}))}$

Step 6.2.2

Cancel the common factor.

$\frac{x ((- 12 x^{4} y^{4} - 3 x^{2} y + 8 x^{4} - 72 y^{2}) \cdot 1)}{x (12 (- 3 x y^{2}))}$

Step 6.2.3

Rewrite the expression.

$\frac{(- 12 x^{4} y^{4} - 3 x^{2} y + 8 x^{4} - 72 y^{2}) \cdot 1}{12 (- 3 x y^{2})}$

Step 7

Multiply

$- 12 x^{4} y^{4} - 3 x^{2} y + 8 x^{4} - 72 y^{2}$ by

$1$ .

$\frac{- 12 x^{4} y^{4} - 3 x^{2} y + 8 x^{4} - 72 y^{2}}{12 (- 3 x y^{2})}$

Step 8

Multiply

$- 3$ by

$12$ .

$\frac{- 12 x^{4} y^{4} - 3 x^{2} y + 8 x^{4} - 72 y^{2}}{- 36 (x y^{2})}$

Step 9

Move the negative in front of the fraction.

$- \frac{- 12 x^{4} y^{4} - 3 x^{2} y + 8 x^{4} - 72 y^{2}}{36 x y^{2}}$

Step 10

Factor

$- 1$ out of

$- 12 x^{4} y^{4}$ .

$- \frac{- (12 x^{4} y^{4}) - 3 x^{2} y + 8 x^{4} - 72 y^{2}}{36 x y^{2}}$

Step 11

Factor

$- 1$ out of

$- 3 x^{2} y$ .

$- \frac{- (12 x^{4} y^{4}) - (3 x^{2} y) + 8 x^{4} - 72 y^{2}}{36 x y^{2}}$

Step 12

Factor

$- 1$ out of

$- (12 x^{4} y^{4}) - (3 x^{2} y)$ .

$- \frac{- (12 x^{4} y^{4} + 3 x^{2} y) + 8 x^{4} - 72 y^{2}}{36 x y^{2}}$

Step 13

Factor

$- 1$ out of

$8 x^{4}$ .

$- \frac{- (12 x^{4} y^{4} + 3 x^{2} y) - (- 8 x^{4}) - 72 y^{2}}{36 x y^{2}}$

Step 14

Factor

$- 1$ out of

$- (12 x^{4} y^{4} + 3 x^{2} y) - (- 8 x^{4})$ .

$- \frac{- (12 x^{4} y^{4} + 3 x^{2} y - 8 x^{4}) - 72 y^{2}}{36 x y^{2}}$

Step 15

Factor

$- 1$ out of

$- 72 y^{2}$ .

$- \frac{- (12 x^{4} y^{4} + 3 x^{2} y - 8 x^{4}) - (72 y^{2})}{36 x y^{2}}$

Step 16

Factor

$- 1$ out of

$- (12 x^{4} y^{4} + 3 x^{2} y - 8 x^{4}) - (72 y^{2})$ .

$- \frac{- (12 x^{4} y^{4} + 3 x^{2} y - 8 x^{4} + 72 y^{2})}{36 x y^{2}}$

Step 17

Rewrite

$- (12 x^{4} y^{4} + 3 x^{2} y - 8 x^{4} + 72 y^{2})$ as

$- 1 (12 x^{4} y^{4} + 3 x^{2} y - 8 x^{4} + 72 y^{2})$ .

$- \frac{- 1 (12 x^{4} y^{4} + 3 x^{2} y - 8 x^{4} + 72 y^{2})}{36 x y^{2}}$

Step 18

Move the negative in front of the fraction.

$- - \frac{12 x^{4} y^{4} + 3 x^{2} y - 8 x^{4} + 72 y^{2}}{36 x y^{2}}$

Step 19

Multiply

$- 1$ by

$- 1$ .

$1 \frac{12 x^{4} y^{4} + 3 x^{2} y - 8 x^{4} + 72 y^{2}}{36 x y^{2}}$

Step 20

Multiply

$\frac{12 x^{4} y^{4} + 3 x^{2} y - 8 x^{4} + 72 y^{2}}{36 x y^{2}}$ by

$1$ .

$\frac{12 x^{4} y^{4} + 3 x^{2} y - 8 x^{4} + 72 y^{2}}{36 x y^{2}}$

Step 21

Split the fraction

$\frac{12 x^{4} y^{4} + 3 x^{2} y - 8 x^{4} + 72 y^{2}}{36 x y^{2}}$ into two fractions.

$\frac{12 x^{4} y^{4} + 3 x^{2} y - 8 x^{4}}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 22

Split the fraction

$\frac{12 x^{4} y^{4} + 3 x^{2} y - 8 x^{4}}{36 x y^{2}}$ into two fractions.

$\frac{12 x^{4} y^{4} + 3 x^{2} y}{36 x y^{2}} + \frac{- 8 x^{4}}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 23

Split the fraction

$\frac{12 x^{4} y^{4} + 3 x^{2} y}{36 x y^{2}}$ into two fractions.

$\frac{12 x^{4} y^{4}}{36 x y^{2}} + \frac{3 x^{2} y}{36 x y^{2}} + \frac{- 8 x^{4}}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 24

Cancel the common factor of

$12$ and

$36$ .

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Step 24.1

Factor

$12$ out of

$12 x^{4} y^{4}$ .

$\frac{12 (x^{4} y^{4})}{36 x y^{2}} + \frac{3 x^{2} y}{36 x y^{2}} + \frac{- 8 x^{4}}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 24.2

Cancel the common factors.

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Step 24.2.1

Factor

$12$ out of

$36 x y^{2}$ .

$\frac{12 (x^{4} y^{4})}{12 (3 x y^{2})} + \frac{3 x^{2} y}{36 x y^{2}} + \frac{- 8 x^{4}}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 24.2.2

Cancel the common factor.

$\frac{12 (x^{4} y^{4})}{12 (3 x y^{2})} + \frac{3 x^{2} y}{36 x y^{2}} + \frac{- 8 x^{4}}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 24.2.3

Rewrite the expression.

$\frac{x^{4} y^{4}}{3 x y^{2}} + \frac{3 x^{2} y}{36 x y^{2}} + \frac{- 8 x^{4}}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 25

Cancel the common factor of

$x^{4}$ and

$x$ .

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Step 25.1

Factor

$x$ out of

$x^{4} y^{4}$ .

$\frac{x (x^{3} y^{4})}{3 x y^{2}} + \frac{3 x^{2} y}{36 x y^{2}} + \frac{- 8 x^{4}}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 25.2

Cancel the common factors.

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Step 25.2.1

Factor

$x$ out of

$3 x y^{2}$ .

$\frac{x (x^{3} y^{4})}{x (3 y^{2})} + \frac{3 x^{2} y}{36 x y^{2}} + \frac{- 8 x^{4}}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 25.2.2

Cancel the common factor.

$\frac{x (x^{3} y^{4})}{x (3 y^{2})} + \frac{3 x^{2} y}{36 x y^{2}} + \frac{- 8 x^{4}}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 25.2.3

Rewrite the expression.

$\frac{x^{3} y^{4}}{3 y^{2}} + \frac{3 x^{2} y}{36 x y^{2}} + \frac{- 8 x^{4}}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 26

Cancel the common factor of

$y^{4}$ and

$y^{2}$ .

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Step 26.1

Factor

$y^{2}$ out of

$x^{3} y^{4}$ .

$\frac{y^{2} (x^{3} y^{2})}{3 y^{2}} + \frac{3 x^{2} y}{36 x y^{2}} + \frac{- 8 x^{4}}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 26.2

Cancel the common factors.

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Step 26.2.1

Factor

$y^{2}$ out of

$3 y^{2}$ .

$\frac{y^{2} (x^{3} y^{2})}{y^{2} \cdot 3} + \frac{3 x^{2} y}{36 x y^{2}} + \frac{- 8 x^{4}}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 26.2.2

Cancel the common factor.

$\frac{y^{2} (x^{3} y^{2})}{y^{2} \cdot 3} + \frac{3 x^{2} y}{36 x y^{2}} + \frac{- 8 x^{4}}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 26.2.3

Rewrite the expression.

$\frac{x^{3} y^{2}}{3} + \frac{3 x^{2} y}{36 x y^{2}} + \frac{- 8 x^{4}}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 27

Cancel the common factor of

$3$ and

$36$ .

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Step 27.1

Factor

$3$ out of

$3 x^{2} y$ .

$\frac{x^{3} y^{2}}{3} + \frac{3 (x^{2} y)}{36 x y^{2}} + \frac{- 8 x^{4}}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 27.2

Cancel the common factors.

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Step 27.2.1

Factor

$3$ out of

$36 x y^{2}$ .

$\frac{x^{3} y^{2}}{3} + \frac{3 (x^{2} y)}{3 (12 x y^{2})} + \frac{- 8 x^{4}}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 27.2.2

Cancel the common factor.

$\frac{x^{3} y^{2}}{3} + \frac{3 (x^{2} y)}{3 (12 x y^{2})} + \frac{- 8 x^{4}}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 27.2.3

Rewrite the expression.

$\frac{x^{3} y^{2}}{3} + \frac{x^{2} y}{12 x y^{2}} + \frac{- 8 x^{4}}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 28

Cancel the common factor of

$x^{2}$ and

$x$ .

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Step 28.1

Factor

$x$ out of

$x^{2} y$ .

$\frac{x^{3} y^{2}}{3} + \frac{x (x y)}{12 x y^{2}} + \frac{- 8 x^{4}}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 28.2

Cancel the common factors.

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Step 28.2.1

Factor

$x$ out of

$12 x y^{2}$ .

$\frac{x^{3} y^{2}}{3} + \frac{x (x y)}{x (12 y^{2})} + \frac{- 8 x^{4}}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 28.2.2

Cancel the common factor.

$\frac{x^{3} y^{2}}{3} + \frac{x (x y)}{x (12 y^{2})} + \frac{- 8 x^{4}}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 28.2.3

Rewrite the expression.

$\frac{x^{3} y^{2}}{3} + \frac{x y}{12 y^{2}} + \frac{- 8 x^{4}}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 29

Cancel the common factor of

$y$ and

$y^{2}$ .

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Step 29.1

Factor

$y$ out of

$x y$ .

$\frac{x^{3} y^{2}}{3} + \frac{y x}{12 y^{2}} + \frac{- 8 x^{4}}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 29.2

Cancel the common factors.

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Step 29.2.1

Factor

$y$ out of

$12 y^{2}$ .

$\frac{x^{3} y^{2}}{3} + \frac{y x}{y (12 y)} + \frac{- 8 x^{4}}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 29.2.2

Cancel the common factor.

$\frac{x^{3} y^{2}}{3} + \frac{y x}{y (12 y)} + \frac{- 8 x^{4}}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 29.2.3

Rewrite the expression.

$\frac{x^{3} y^{2}}{3} + \frac{x}{12 y} + \frac{- 8 x^{4}}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 30

Cancel the common factor of

$- 8$ and

$36$ .

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Step 30.1

Factor

$4$ out of

$- 8 x^{4}$ .

$\frac{x^{3} y^{2}}{3} + \frac{x}{12 y} + \frac{4 (- 2 x^{4})}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 30.2

Cancel the common factors.

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Step 30.2.1

Factor

$4$ out of

$36 x y^{2}$ .

$\frac{x^{3} y^{2}}{3} + \frac{x}{12 y} + \frac{4 (- 2 x^{4})}{4 (9 x y^{2})} + \frac{72 y^{2}}{36 x y^{2}}$

Step 30.2.2

Cancel the common factor.

$\frac{x^{3} y^{2}}{3} + \frac{x}{12 y} + \frac{4 (- 2 x^{4})}{4 (9 x y^{2})} + \frac{72 y^{2}}{36 x y^{2}}$

Step 30.2.3

Rewrite the expression.

$\frac{x^{3} y^{2}}{3} + \frac{x}{12 y} + \frac{- 2 x^{4}}{9 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 31

Cancel the common factor of

$x^{4}$ and

$x$ .

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Step 31.1

Factor

$x$ out of

$- 2 x^{4}$ .

$\frac{x^{3} y^{2}}{3} + \frac{x}{12 y} + \frac{x (- 2 x^{3})}{9 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 31.2

Cancel the common factors.

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Step 31.2.1

Factor

$x$ out of

$9 x y^{2}$ .

$\frac{x^{3} y^{2}}{3} + \frac{x}{12 y} + \frac{x (- 2 x^{3})}{x (9 y^{2})} + \frac{72 y^{2}}{36 x y^{2}}$

Step 31.2.2

Cancel the common factor.

$\frac{x^{3} y^{2}}{3} + \frac{x}{12 y} + \frac{x (- 2 x^{3})}{x (9 y^{2})} + \frac{72 y^{2}}{36 x y^{2}}$

Step 31.2.3

Rewrite the expression.

$\frac{x^{3} y^{2}}{3} + \frac{x}{12 y} + \frac{- 2 x^{3}}{9 y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 32

Move the negative in front of the fraction.

$\frac{x^{3} y^{2}}{3} + \frac{x}{12 y} - \frac{2 x^{3}}{9 y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 33

Cancel the common factor of

$72$ and

$36$ .

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Step 33.1

Factor

$36$ out of

$72 y^{2}$ .

$\frac{x^{3} y^{2}}{3} + \frac{x}{12 y} - \frac{2 x^{3}}{9 y^{2}} + \frac{36 (2 y^{2})}{36 x y^{2}}$

Step 33.2

Cancel the common factors.

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Step 33.2.1

Factor

$36$ out of

$36 x y^{2}$ .

$\frac{x^{3} y^{2}}{3} + \frac{x}{12 y} - \frac{2 x^{3}}{9 y^{2}} + \frac{36 (2 y^{2})}{36 (x y^{2})}$

Step 33.2.2

Cancel the common factor.

$\frac{x^{3} y^{2}}{3} + \frac{x}{12 y} - \frac{2 x^{3}}{9 y^{2}} + \frac{36 (2 y^{2})}{36 (x y^{2})}$

Step 33.2.3

Rewrite the expression.

$\frac{x^{3} y^{2}}{3} + \frac{x}{12 y} - \frac{2 x^{3}}{9 y^{2}} + \frac{2 y^{2}}{x y^{2}}$

Step 34

Cancel the common factor of

$y^{2}$ .

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Step 34.1

Cancel the common factor.

$\frac{x^{3} y^{2}}{3} + \frac{x}{12 y} - \frac{2 x^{3}}{9 y^{2}} + \frac{2 y^{2}}{x y^{2}}$

Step 34.2

Rewrite the expression.

$\frac{x^{3} y^{2}}{3} + \frac{x}{12 y} - \frac{2 x^{3}}{9 y^{2}} + \frac{2}{x}$