Pre-Algebra Examples

$\frac{\frac{y - 3}{y^{2}}}{\frac{y^{2} - 9}{5 y}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{y - 3}{y^{2}} \cdot \frac{5 y}{y^{2} - 9}$

Step 2

Cancel the common factor of $y$ .

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Step 2.1

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

$\frac{y - 3}{y \cdot y} \cdot \frac{5 y}{y^{2} - 9}$

Step 2.2

Factor $y$ out of $5 y$ .

$\frac{y - 3}{y \cdot y} \cdot \frac{y \cdot 5}{y^{2} - 9}$

Step 2.3

Cancel the common factor.

$\frac{y - 3}{y \cdot y} \cdot \frac{y \cdot 5}{y^{2} - 9}$

Step 2.4

Rewrite the expression.

$\frac{y - 3}{y} \cdot \frac{5}{y^{2} - 9}$

Step 3

Multiply $\frac{y - 3}{y}$ by $\frac{5}{y^{2} - 9}$ .

$\frac{(y - 3) \cdot 5}{y (y^{2} - 9)}$

Step 4

Simplify the denominator.

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Step 4.1

Rewrite $9$ as $3^{2}$ .

$\frac{(y - 3) \cdot 5}{y (y^{2} - 3^{2})}$

Step 4.2

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 $b = 3$ .

$\frac{(y - 3) \cdot 5}{y (y + 3) (y - 3)}$

Step 5

Cancel the common factor of $y - 3$ .

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Step 5.1

Cancel the common factor.

$\frac{(y - 3) \cdot 5}{y (y + 3) (y - 3)}$

Step 5.2

Rewrite the expression.

$\frac{5}{y (y + 3)}$