Pre-Algebra Examples

$(- 7 x^{2} y^{3} + 21 x y^{2}) \div (- 3 x^{2} y^{3})$

Step 1

Rewrite the division as a fraction.

$\frac{- 7 x^{2} y^{3} + 21 x y^{2}}{- 3 x^{2} y^{3}}$

Step 2

Factor $7 x y^{2}$ out of $- 7 x^{2} y^{3} + 21 x y^{2}$ .

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Step 2.1

Factor $7 x y^{2}$ out of $- 7 x^{2} y^{3}$ .

$\frac{7 x y^{2} (- x y) + 21 x y^{2}}{- 3 x^{2} y^{3}}$

Step 2.2

Factor $7 x y^{2}$ out of $21 x y^{2}$ .

$\frac{7 x y^{2} (- x y) + 7 x y^{2} (3)}{- 3 x^{2} y^{3}}$

Step 2.3

Factor $7 x y^{2}$ out of $7 x y^{2} (- x y) + 7 x y^{2} (3)$ .

$\frac{7 x y^{2} (- x y + 3)}{- 3 x^{2} y^{3}}$

Step 3

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

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Step 3.1

Factor $x$ out of $7 x y^{2} (- x y + 3)$ .

$\frac{x (7 y^{2} (- x y + 3))}{- 3 x^{2} y^{3}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $x$ out of $- 3 x^{2} y^{3}$ .

$\frac{x (7 y^{2} (- x y + 3))}{x (- 3 x y^{3})}$

Step 3.2.2

Cancel the common factor.

$\frac{x (7 y^{2} (- x y + 3))}{x (- 3 x y^{3})}$

Step 3.2.3

Rewrite the expression.

$\frac{7 y^{2} (- x y + 3)}{- 3 x y^{3}}$

Step 4

Cancel the common factor of $y^{2}$ and $y^{3}$ .

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Step 4.1

Factor $y^{2}$ out of $7 y^{2} (- x y + 3)$ .

$\frac{y^{2} (7 (- x y + 3))}{- 3 x y^{3}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $y^{2}$ out of $- 3 x y^{3}$ .

$\frac{y^{2} (7 (- x y + 3))}{y^{2} (- 3 x y)}$

Step 4.2.2

Cancel the common factor.

$\frac{y^{2} (7 (- x y + 3))}{y^{2} (- 3 x y)}$

Step 4.2.3

Rewrite the expression.

$\frac{7 (- x y + 3)}{- 3 x y}$

Step 5

Move the negative in front of the fraction.

$- \frac{7 (- x y + 3)}{3 x y}$

Step 6

Factor $- 1$ out of $- x y$ .

$- \frac{7 (- (x y) + 3)}{3 x y}$

Step 7

Rewrite $3$ as $- 1 (- 3)$ .

$- \frac{7 (- (x y) - 1 (- 3))}{3 x y}$

Step 8

Factor $- 1$ out of $- (x y) - 1 (- 3)$ .

$- \frac{7 (- (x y - 3))}{3 x y}$

Step 9

Rewrite $- (x y - 3)$ as $- 1 (x y - 3)$ .

$- \frac{7 (- 1 (x y - 3))}{3 x y}$

Step 10

Move the negative in front of the fraction.

$- - \frac{7 (x y - 3)}{3 x y}$

Step 11

Multiply $- 1$ by $- 1$ .

$1 \frac{7 (x y - 3)}{3 x y}$

Step 12

Multiply $\frac{7 (x y - 3)}{3 x y}$ by $1$ .

$\frac{7 (x y - 3)}{3 x y}$

Step 13

Apply the distributive property.

$\frac{7 (x y) + 7 \cdot - 3}{3 x y}$

Step 14

Multiply $7$ by $- 3$ .

$\frac{7 x y - 21}{3 x y}$

Step 15

Split the fraction $\frac{7 x y - 21}{3 x y}$ into two fractions.

$\frac{7 x y}{3 x y} + \frac{- 21}{3 x y}$

Step 16

Cancel the common factor of $x$ .

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Step 16.1

Cancel the common factor.

$\frac{7 x y}{3 x y} + \frac{- 21}{3 x y}$

Step 16.2

Rewrite the expression.

$\frac{7 y}{3 y} + \frac{- 21}{3 x y}$

Step 17

Cancel the common factor of $y$ .

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Step 17.1

Cancel the common factor.

$\frac{7 y}{3 y} + \frac{- 21}{3 x y}$

Step 17.2

Rewrite the expression.

$\frac{7}{3} + \frac{- 21}{3 x y}$

Step 18

Cancel the common factor of $- 21$ and $3$ .

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Step 18.1

Factor $3$ out of $- 21$ .

$\frac{7}{3} + \frac{3 \cdot - 7}{3 x y}$

Step 18.2

Cancel the common factors.

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Step 18.2.1

Factor $3$ out of $3 x y$ .

$\frac{7}{3} + \frac{3 \cdot - 7}{3 (x y)}$

Step 18.2.2

Cancel the common factor.

$\frac{7}{3} + \frac{3 \cdot - 7}{3 (x y)}$

Step 18.2.3

Rewrite the expression.

$\frac{7}{3} + \frac{- 7}{x y}$

Step 19

Move the negative in front of the fraction.

$\frac{7}{3} - \frac{7}{x y}$