Pre-Algebra Examples

$\frac{5 x^{2} + 10 x^{2} y^{2} - x y^{2}}{5 x y}$

Step 1

Simplify the numerator.

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Step 1.1

Factor $x$ out of $5 x^{2} + 10 x^{2} y^{2} - x y^{2}$ .

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Step 1.1.1

Factor $x$ out of $5 x^{2}$ .

$\frac{x (5 x) + 10 x^{2} y^{2} - x y^{2}}{5 x y}$

Step 1.1.2

Factor $x$ out of $10 x^{2} y^{2}$ .

$\frac{x (5 x) + x (10 x y^{2}) - x y^{2}}{5 x y}$

Step 1.1.3

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

$\frac{x (5 x) + x (10 x y^{2}) + x (- 1 y^{2})}{5 x y}$

Step 1.1.4

Factor $x$ out of $x (5 x) + x (10 x y^{2})$ .

$\frac{x (5 x + 10 x y^{2}) + x (- 1 y^{2})}{5 x y}$

Step 1.1.5

Factor $x$ out of $x (5 x + 10 x y^{2}) + x (- 1 y^{2})$ .

$\frac{x (5 x + 10 x y^{2} - 1 y^{2})}{5 x y}$

Step 1.2

Rewrite $- 1 y^{2}$ as $- y^{2}$ .

$\frac{x (5 x + 10 x y^{2} - y^{2})}{5 x y}$

Step 2

Cancel the common factor of $x$ .

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Step 2.1

Cancel the common factor.

$\frac{x (5 x + 10 x y^{2} - y^{2})}{5 x y}$

Step 2.2

Rewrite the expression.

$\frac{5 x + 10 x y^{2} - y^{2}}{5 y}$

Step 3

Split the fraction $\frac{5 x + 10 x y^{2} - y^{2}}{5 y}$ into two fractions.

$\frac{5 x + 10 x y^{2}}{5 y} + \frac{- y^{2}}{5 y}$

Step 4

Split the fraction $\frac{5 x + 10 x y^{2}}{5 y}$ into two fractions.

$\frac{5 x}{5 y} + \frac{10 x y^{2}}{5 y} + \frac{- y^{2}}{5 y}$

Step 5

Cancel the common factor of $5$ .

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Step 5.1

Cancel the common factor.

$\frac{5 x}{5 y} + \frac{10 x y^{2}}{5 y} + \frac{- y^{2}}{5 y}$

Step 5.2

Rewrite the expression.

$\frac{x}{y} + \frac{10 x y^{2}}{5 y} + \frac{- y^{2}}{5 y}$

Step 6

Cancel the common factor of $10$ and $5$ .

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Step 6.1

Factor $5$ out of $10 x y^{2}$ .

$\frac{x}{y} + \frac{5 (2 x y^{2})}{5 y} + \frac{- y^{2}}{5 y}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $5$ out of $5 y$ .

$\frac{x}{y} + \frac{5 (2 x y^{2})}{5 (y)} + \frac{- y^{2}}{5 y}$

Step 6.2.2

Cancel the common factor.

$\frac{x}{y} + \frac{5 (2 x y^{2})}{5 y} + \frac{- y^{2}}{5 y}$

Step 6.2.3

Rewrite the expression.

$\frac{x}{y} + \frac{2 x y^{2}}{y} + \frac{- y^{2}}{5 y}$

Step 7

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

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Step 7.1

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

$\frac{x}{y} + \frac{y (2 x y)}{y} + \frac{- y^{2}}{5 y}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Raise $y$ to the power of $1$ .

$\frac{x}{y} + \frac{y (2 x y)}{y^{1}} + \frac{- y^{2}}{5 y}$

Step 7.2.2

Factor $y$ out of $y^{1}$ .

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

Step 7.2.3

Cancel the common factor.

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

Step 7.2.4

Rewrite the expression.

$\frac{x}{y} + \frac{2 x y}{1} + \frac{- y^{2}}{5 y}$

Step 7.2.5

Divide $2 x y$ by $1$ .

$\frac{x}{y} + 2 x y + \frac{- y^{2}}{5 y}$

Step 8

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

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Step 8.1

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

$\frac{x}{y} + 2 x y + \frac{y (- y)}{5 y}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $y$ out of $5 y$ .

$\frac{x}{y} + 2 x y + \frac{y (- y)}{y \cdot 5}$

Step 8.2.2

Cancel the common factor.

$\frac{x}{y} + 2 x y + \frac{y (- y)}{y \cdot 5}$

Step 8.2.3

Rewrite the expression.

$\frac{x}{y} + 2 x y + \frac{- y}{5}$

Step 9

Move the negative in front of the fraction.

$\frac{x}{y} + 2 x y - \frac{y}{5}$