Algebra Examples

$\frac{y^{2}}{y^{2} + 2 y} - \frac{4}{y^{2} + 2 y}$

Step 1

Combine the numerators over the common denominator.

$\frac{y^{2} - 4}{y^{2} + 2 y}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $4$ as $2^{2}$ .

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

Step 2.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = y$ and $b = 2$ .

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

Step 3

Simplify terms.

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Step 3.1

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

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Step 3.1.1

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

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

Step 3.1.2

Factor $y$ out of $2 y$ .

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

Step 3.1.3

Factor $y$ out of $y \cdot y + y \cdot 2$ .

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

Step 3.2

Cancel the common factor of $y + 2$ .

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Step 3.2.1

Cancel the common factor.

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

Step 3.2.2

Rewrite the expression.

$\frac{y - 2}{y}$