Basic Math Examples

$\frac{25 y^{2} - 36}{56 y} \div \frac{5 y - 6}{8 y}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{25 y^{2} - 36}{56 y} \cdot \frac{8 y}{5 y - 6}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $8 y$ .

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Step 2.1.1

Factor $8 y$ out of $56 y$ .

$\frac{25 y^{2} - 36}{8 y (7)} \cdot \frac{8 y}{5 y - 6}$

Step 2.1.2

Cancel the common factor.

$\frac{25 y^{2} - 36}{8 y \cdot 7} \cdot \frac{8 y}{5 y - 6}$

Step 2.1.3

Rewrite the expression.

$\frac{25 y^{2} - 36}{7} \cdot \frac{1}{5 y - 6}$

Step 2.2

Multiply $\frac{25 y^{2} - 36}{7}$ by $\frac{1}{5 y - 6}$ .

$\frac{25 y^{2} - 36}{7 (5 y - 6)}$

Step 3

Simplify the numerator.

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Step 3.1

Rewrite $25 y^{2}$ as ${(5 y)}^{2}$ .

$\frac{{(5 y)}^{2} - 36}{7 (5 y - 6)}$

Step 3.2

Rewrite $36$ as $6^{2}$ .

$\frac{{(5 y)}^{2} - 6^{2}}{7 (5 y - 6)}$

Step 3.3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 5 y$ and $b = 6$ .

$\frac{(5 y + 6) (5 y - 6)}{7 (5 y - 6)}$

Step 4

Cancel the common factor of $5 y - 6$ .

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Step 4.1

Cancel the common factor.

$\frac{(5 y + 6) (5 y - 6)}{7 (5 y - 6)}$

Step 4.2

Rewrite the expression.

$\frac{5 y + 6}{7}$