Basic Math Examples

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

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{y}{y - z} \cdot \frac{y^{2} - z^{2}}{y^{2}}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $y$ .

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Step 2.1.1

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

$\frac{y}{y - z} \cdot \frac{y^{2} - z^{2}}{y \cdot y}$

Step 2.1.2

Cancel the common factor.

$\frac{y}{y - z} \cdot \frac{y^{2} - z^{2}}{y \cdot y}$

Step 2.1.3

Rewrite the expression.

$\frac{1}{y - z} \cdot \frac{y^{2} - z^{2}}{y}$

Step 2.2

Multiply $\frac{1}{y - z}$ by $\frac{y^{2} - z^{2}}{y}$ .

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

Step 3

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 $b = z$ .

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

Step 4

Cancel the common factor of $y - z$ .

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Step 4.1

Cancel the common factor.

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

Step 4.2

Rewrite the expression.

$\frac{y + z}{y}$