Pre-Algebra Examples

$\frac{9 x^{2} - 6 x^{3} y^{2} + 12 x y^{3}}{18 x y}$

Step 1

Factor $3 x$ out of $9 x^{2} - 6 x^{3} y^{2} + 12 x y^{3}$ .

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Step 1.1

Factor $3 x$ out of $9 x^{2}$ .

$\frac{3 x (3 x) - 6 x^{3} y^{2} + 12 x y^{3}}{18 x y}$

Step 1.2

Factor $3 x$ out of $- 6 x^{3} y^{2}$ .

$\frac{3 x (3 x) + 3 x (- 2 x^{2} y^{2}) + 12 x y^{3}}{18 x y}$

Step 1.3

Factor $3 x$ out of $12 x y^{3}$ .

$\frac{3 x (3 x) + 3 x (- 2 x^{2} y^{2}) + 3 x (4 y^{3})}{18 x y}$

Step 1.4

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

$\frac{3 x (3 x - 2 x^{2} y^{2}) + 3 x (4 y^{3})}{18 x y}$

Step 1.5

Factor $3 x$ out of $3 x (3 x - 2 x^{2} y^{2}) + 3 x (4 y^{3})$ .

$\frac{3 x (3 x - 2 x^{2} y^{2} + 4 y^{3})}{18 x y}$

Step 2

Cancel the common factor of $3$ and $18$ .

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Step 2.1

Factor $3$ out of $3 x (3 x - 2 x^{2} y^{2} + 4 y^{3})$ .

$\frac{3 (x (3 x - 2 x^{2} y^{2} + 4 y^{3}))}{18 x y}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $3$ out of $18 x y$ .

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

Step 3

Cancel the common factor of $x$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

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

Step 4

Split the fraction $\frac{3 x - 2 x^{2} y^{2} + 4 y^{3}}{6 y}$ into two fractions.

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

Step 5

Split the fraction $\frac{3 x - 2 x^{2} y^{2}}{6 y}$ into two fractions.

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

Step 6

Cancel the common factor of $3$ and $6$ .

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Step 6.1

Factor $3$ out of $3 x$ .

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

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $3$ out of $6 y$ .

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

Step 6.2.2

Cancel the common factor.

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

Step 6.2.3

Rewrite the expression.

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

Step 7

Cancel the common factor of $- 2$ and $6$ .

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Step 7.1

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

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

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $2$ out of $6 y$ .

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

Step 7.2.2

Cancel the common factor.

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

Step 7.2.3

Rewrite the expression.

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

Step 8

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

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Step 8.1

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

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

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $y$ out of $3 y$ .

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

Step 8.2.2

Cancel the common factor.

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

Step 8.2.3

Rewrite the expression.

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

Step 9

Move the negative in front of the fraction.

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

Step 10

Cancel the common factor of $4$ and $6$ .

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Step 10.1

Factor $2$ out of $4 y^{3}$ .

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

Step 10.2

Cancel the common factors.

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Step 10.2.1

Factor $2$ out of $6 y$ .

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

Step 10.2.2

Cancel the common factor.

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

Step 10.2.3

Rewrite the expression.

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

Step 11

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

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Step 11.1

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

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

Step 11.2

Cancel the common factors.

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Step 11.2.1

Factor $y$ out of $3 y$ .

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

Step 11.2.2

Cancel the common factor.

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

Step 11.2.3

Rewrite the expression.

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