Pre-Algebra Examples

$\frac{- 36 v^{7} x^{2} + 12 v^{5} x^{4} \cdot (24 v^{7} x^{6})}{4 v^{5} x^{4}}$

Step 1

Simplify the numerator.

Tap for more steps...

Step 1.1

Factor $12 v^{5} x^{2}$ out of $- 36 v^{7} x^{2} + 12 v^{5} x^{4} \cdot (24 v^{7} x^{6})$ .

Tap for more steps...

Step 1.1.1

Factor $12 v^{5} x^{2}$ out of $- 36 v^{7} x^{2}$ .

$\frac{12 v^{5} x^{2} (- 3 v^{2}) + 12 v^{5} x^{4} \cdot (24 v^{7} x^{6})}{4 v^{5} x^{4}}$

Step 1.1.2

Factor $12 v^{5} x^{2}$ out of $12 v^{5} x^{4} \cdot (24 v^{7} x^{6})$ .

$\frac{12 v^{5} x^{2} (- 3 v^{2}) + 12 v^{5} x^{2} (x^{2} \cdot (24 v^{7} x^{6}))}{4 v^{5} x^{4}}$

Step 1.1.3

Factor $12 v^{5} x^{2}$ out of $12 v^{5} x^{2} (- 3 v^{2}) + 12 v^{5} x^{2} (x^{2} \cdot (24 v^{7} x^{6}))$ .

$\frac{12 v^{5} x^{2} (- 3 v^{2} + x^{2} \cdot (24 v^{7} x^{6}))}{4 v^{5} x^{4}}$

Step 1.2

Multiply $x^{2}$ by $x^{6}$ by adding the exponents.

Tap for more steps...

Step 1.2.1

Move $x^{6}$ .

$\frac{12 v^{5} x^{2} (- 3 v^{2} + x^{6} x^{2} \cdot (24 v^{7}))}{4 v^{5} x^{4}}$

Step 1.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{12 v^{5} x^{2} (- 3 v^{2} + x^{6 + 2} \cdot (24 v^{7}))}{4 v^{5} x^{4}}$

Step 1.2.3

Add $6$ and $2$ .

$\frac{12 v^{5} x^{2} (- 3 v^{2} + x^{8} \cdot (24 v^{7}))}{4 v^{5} x^{4}}$

Step 1.3

Rewrite using the commutative property of multiplication.

$\frac{12 v^{5} x^{2} (- 3 v^{2} + 24 x^{8} v^{7})}{4 v^{5} x^{4}}$

Step 1.4

Factor $3 v^{2}$ out of $- 3 v^{2} + 24 x^{8} v^{7}$ .

Tap for more steps...

Step 1.4.1

Factor $3 v^{2}$ out of $- 3 v^{2}$ .

$\frac{12 v^{5} x^{2} (3 v^{2} (- 1) + 24 x^{8} v^{7})}{4 v^{5} x^{4}}$

Step 1.4.2

Factor $3 v^{2}$ out of $24 x^{8} v^{7}$ .

$\frac{12 v^{5} x^{2} (3 v^{2} (- 1) + 3 v^{2} (8 x^{8} v^{5}))}{4 v^{5} x^{4}}$

Step 1.4.3

Factor $3 v^{2}$ out of $3 v^{2} (- 1) + 3 v^{2} (8 x^{8} v^{5})$ .

$\frac{12 v^{5} x^{2} (3 v^{2} (- 1 + 8 x^{8} v^{5}))}{4 v^{5} x^{4}}$

$\frac{12 v^{5} x^{2} \cdot 3 v^{2} (- 1 + 8 x^{8} v^{5})}{4 v^{5} x^{4}}$

Step 1.5

Combine exponents.

Tap for more steps...

Step 1.5.1

Multiply $3$ by $12$ .

$\frac{36 v^{5} x^{2} v^{2} (- 1 + 8 x^{8} v^{5})}{4 v^{5} x^{4}}$

Step 1.5.2

Multiply $v^{5}$ by $v^{2}$ by adding the exponents.

Tap for more steps...

Step 1.5.2.1

Move $v^{2}$ .

$\frac{36 (v^{2} v^{5}) x^{2} (- 1 + 8 x^{8} v^{5})}{4 v^{5} x^{4}}$

Step 1.5.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{36 v^{2 + 5} x^{2} (- 1 + 8 x^{8} v^{5})}{4 v^{5} x^{4}}$

Step 1.5.2.3

Add $2$ and $5$ .

$\frac{36 v^{7} x^{2} (- 1 + 8 x^{8} v^{5})}{4 v^{5} x^{4}}$

Step 2

Cancel the common factor of $36$ and $4$ .

Tap for more steps...

Step 2.1

Factor $4$ out of $36 v^{7} x^{2} (- 1 + 8 x^{8} v^{5})$ .

$\frac{4 (9 v^{7} x^{2} (- 1 + 8 x^{8} v^{5}))}{4 v^{5} x^{4}}$

Step 2.2

Cancel the common factors.

Tap for more steps...

Step 2.2.1

Factor $4$ out of $4 v^{5} x^{4}$ .

$\frac{4 (9 v^{7} x^{2} (- 1 + 8 x^{8} v^{5}))}{4 (v^{5} x^{4})}$

Step 2.2.2

Cancel the common factor.

$\frac{4 (9 v^{7} x^{2} (- 1 + 8 x^{8} v^{5}))}{4 (v^{5} x^{4})}$

Step 2.2.3

Rewrite the expression.

$\frac{9 v^{7} x^{2} (- 1 + 8 x^{8} v^{5})}{v^{5} x^{4}}$

Step 3

Cancel the common factor of $v^{7}$ and $v^{5}$ .

Tap for more steps...

Step 3.1

Factor $v^{5}$ out of $9 v^{7} x^{2} (- 1 + 8 x^{8} v^{5})$ .

$\frac{v^{5} (9 v^{2} x^{2} (- 1 + 8 x^{8} v^{5}))}{v^{5} x^{4}}$

Step 3.2

Cancel the common factors.

Tap for more steps...

Step 3.2.1

Factor $v^{5}$ out of $v^{5} x^{4}$ .

$\frac{v^{5} (9 v^{2} x^{2} (- 1 + 8 x^{8} v^{5}))}{v^{5} (x^{4})}$

Step 3.2.2

Cancel the common factor.

$\frac{v^{5} (9 v^{2} x^{2} (- 1 + 8 x^{8} v^{5}))}{v^{5} x^{4}}$

Step 3.2.3

Rewrite the expression.

$\frac{9 v^{2} x^{2} (- 1 + 8 x^{8} v^{5})}{x^{4}}$

Step 4

Cancel the common factor of $x^{2}$ and $x^{4}$ .

Tap for more steps...

Step 4.1

Factor $x^{2}$ out of $9 v^{2} x^{2} (- 1 + 8 x^{8} v^{5})$ .

$\frac{x^{2} (9 v^{2} (- 1 + 8 x^{8} v^{5}))}{x^{4}}$

Step 4.2

Cancel the common factors.

Tap for more steps...

Step 4.2.1

Factor $x^{2}$ out of $x^{4}$ .

$\frac{x^{2} (9 v^{2} (- 1 + 8 x^{8} v^{5}))}{x^{2} x^{2}}$

Step 4.2.2

Cancel the common factor.

$\frac{x^{2} (9 v^{2} (- 1 + 8 x^{8} v^{5}))}{x^{2} x^{2}}$

Step 4.2.3

Rewrite the expression.

$\frac{9 v^{2} (- 1 + 8 x^{8} v^{5})}{x^{2}}$

Step 5

Rewrite $- 1$ as $- 1 (1)$ .

$\frac{9 v^{2} (- 1 (1) + 8 x^{8} v^{5})}{x^{2}}$

Step 6

Factor $- 1$ out of $8 x^{8} v^{5}$ .

$\frac{9 v^{2} (- 1 (1) - (- 8 x^{8} v^{5}))}{x^{2}}$

Step 7

Factor $- 1$ out of $- 1 (1) - (- 8 x^{8} v^{5})$ .

$\frac{9 v^{2} (- 1 (1 - 8 x^{8} v^{5}))}{x^{2}}$

Step 8

Move the negative in front of the fraction.

$- \frac{(9 v^{2}) (1 - 8 x^{8} v^{5})}{x^{2}}$

Step 9

Reorder factors in $- \frac{(9 v^{2}) (1 - 8 x^{8} v^{5})}{x^{2}}$ .

$- \frac{9 v^{2} (1 - 8 x^{8} v^{5})}{x^{2}}$

Step 10

Apply the distributive property.

$- \frac{9 v^{2} \cdot 1 + 9 v^{2} (- 8 x^{8} v^{5})}{x^{2}}$

Step 11

Multiply $9$ by $1$ .

$- \frac{9 v^{2} + 9 v^{2} (- 8 x^{8} v^{5})}{x^{2}}$

Step 12

Multiply $v^{2}$ by $v^{5}$ by adding the exponents.

Tap for more steps...

Step 12.1

Move $v^{5}$ .

$- \frac{9 v^{2} + 9 (v^{5} v^{2}) (- 8 x^{8})}{x^{2}}$

Step 12.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- \frac{9 v^{2} + 9 v^{5 + 2} (- 8 x^{8})}{x^{2}}$

Step 12.3

Add $5$ and $2$ .

$- \frac{9 v^{2} + 9 v^{7} (- 8 x^{8})}{x^{2}}$

Step 13

Simplify each term.

Tap for more steps...

Step 13.1

Rewrite using the commutative property of multiplication.

$- \frac{9 v^{2} + 9 \cdot - 8 v^{7} x^{8}}{x^{2}}$

Step 13.2

Multiply $9$ by $- 8$ .

$- \frac{9 v^{2} - 72 v^{7} x^{8}}{x^{2}}$

Step 14

Split the fraction $\frac{9 v^{2} - 72 v^{7} x^{8}}{x^{2}}$ into two fractions.

$- (\frac{9 v^{2}}{x^{2}} + \frac{- 72 v^{7} x^{8}}{x^{2}})$

Step 15

Cancel the common factor of $x^{8}$ and $x^{2}$ .

Tap for more steps...

Step 15.1

Factor $x^{2}$ out of $- 72 v^{7} x^{8}$ .

$- (\frac{9 v^{2}}{x^{2}} + \frac{x^{2} (- 72 v^{7} x^{6})}{x^{2}})$

Step 15.2

Cancel the common factors.

Tap for more steps...

Step 15.2.1

Multiply by $1$ .

$- (\frac{9 v^{2}}{x^{2}} + \frac{x^{2} (- 72 v^{7} x^{6})}{x^{2} \cdot 1})$

Step 15.2.2

Cancel the common factor.

$- (\frac{9 v^{2}}{x^{2}} + \frac{x^{2} (- 72 v^{7} x^{6})}{x^{2} \cdot 1})$

Step 15.2.3

Rewrite the expression.

$- (\frac{9 v^{2}}{x^{2}} + \frac{- 72 v^{7} x^{6}}{1})$

Step 15.2.4

Divide $- 72 v^{7} x^{6}$ by $1$ .

$- (\frac{9 v^{2}}{x^{2}} - 72 v^{7} x^{6})$