Algebra Examples

$\frac{5 x^{2} y + 15 x^{2} y^{2} - x y^{2}}{5 x y}$

Step 1

Simplify the numerator.

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Step 1.1

Factor $x y$ out of $5 x^{2} y + 15 x^{2} y^{2} - x y^{2}$ .

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Step 1.1.1

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

$\frac{x y (5 x) + 15 x^{2} y^{2} - x y^{2}}{5 x y}$

Step 1.1.2

Factor $x y$ out of $15 x^{2} y^{2}$ .

$\frac{x y (5 x) + x y (15 x y) - x y^{2}}{5 x y}$

Step 1.1.3

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

$\frac{x y (5 x) + x y (15 x y) + x y (- 1 y)}{5 x y}$

Step 1.1.4

Factor $x y$ out of $x y (5 x) + x y (15 x y)$ .

$\frac{x y (5 x + 15 x y) + x y (- 1 y)}{5 x y}$

Step 1.1.5

Factor $x y$ out of $x y (5 x + 15 x y) + x y (- 1 y)$ .

$\frac{x y (5 x + 15 x y - 1 y)}{5 x y}$

Step 1.2

Rewrite $- 1 y$ as $- y$ .

$\frac{x y (5 x + 15 x y - y)}{5 x y}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Cancel the common factor of $x$ .

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Step 2.1.1

Cancel the common factor.

$\frac{x y (5 x + 15 x y - y)}{5 x y}$

Step 2.1.2

Rewrite the expression.

$\frac{y (5 x + 15 x y - y)}{5 y}$

Step 2.2

Cancel the common factor of $y$ .

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Step 2.2.1

Cancel the common factor.

$\frac{y (5 x + 15 x y - y)}{5 y}$

Step 2.2.2

Rewrite the expression.

$\frac{5 x + 15 x y - y}{5}$