Basic Math Examples

$\frac{\frac{y + 5}{12}}{\frac{25 - y^{2}}{3}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{y + 5}{12} \cdot \frac{3}{25 - y^{2}}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $3$ .

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Step 2.1.1

Factor $3$ out of $12$ .

$\frac{y + 5}{3 (4)} \cdot \frac{3}{25 - y^{2}}$

Step 2.1.2

Cancel the common factor.

$\frac{y + 5}{3 \cdot 4} \cdot \frac{3}{25 - y^{2}}$

Step 2.1.3

Rewrite the expression.

$\frac{y + 5}{4} \cdot \frac{1}{25 - y^{2}}$

Step 2.2

Multiply $\frac{y + 5}{4}$ by $\frac{1}{25 - y^{2}}$ .

$\frac{y + 5}{4 (25 - y^{2})}$

Step 3

Simplify the denominator.

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Step 3.1

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

$\frac{y + 5}{4 (5^{2} - y^{2})}$

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 $a = 5$ and $b = y$ .

$\frac{y + 5}{4 (5 + y) (5 - y)}$

Step 4

Cancel the common factor of $y + 5$ and $5 + y$ .

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Step 4.1

Reorder terms.

$\frac{y + 5}{4 (y + 5) (5 - y)}$

Step 4.2

Cancel the common factor.

$\frac{y + 5}{4 (y + 5) (5 - y)}$

Step 4.3

Rewrite the expression.

$\frac{1}{4 (5 - y)}$