Basic Math Examples

$\frac{\frac{8}{{(y + 5)}^{2}}}{\frac{24}{y^{2} - 25}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{8}{{(y + 5)}^{2}} \cdot \frac{y^{2} - 25}{24}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $8$ .

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Step 2.1.1

Factor $8$ out of $24$ .

$\frac{8}{{(y + 5)}^{2}} \cdot \frac{y^{2} - 25}{8 (3)}$

Step 2.1.2

Cancel the common factor.

$\frac{8}{{(y + 5)}^{2}} \cdot \frac{y^{2} - 25}{8 \cdot 3}$

Step 2.1.3

Rewrite the expression.

$\frac{1}{{(y + 5)}^{2}} \cdot \frac{y^{2} - 25}{3}$

Step 2.2

Multiply $\frac{1}{{(y + 5)}^{2}}$ by $\frac{y^{2} - 25}{3}$ .

$\frac{y^{2} - 25}{{(y + 5)}^{2} \cdot 3}$

Step 3

Simplify the numerator.

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Step 3.1

Rewrite $25$ as $5^{2}$ .

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

Step 3.2

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 $b = 5$ .

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

Step 4

Cancel the common factors.

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Step 4.1

Factor $y + 5$ out of ${(y + 5)}^{2} \cdot 3$ .

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

Step 4.2

Cancel the common factor.

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

Step 4.3

Rewrite the expression.

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

Step 5

Move $3$ to the left of $y + 5$ .

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