Algebra Examples

$\frac{y^{2} - 36}{y^{2} - 49} \div \frac{y + 6}{y + 7}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{y^{2} - 36}{y^{2} - 49} \cdot \frac{y + 7}{y + 6}$

Step 2

Simplify the numerator.

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Step 2.1

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

$\frac{y^{2} - 6^{2}}{y^{2} - 49} \cdot \frac{y + 7}{y + 6}$

Step 2.2

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 $b = 6$ .

$\frac{(y + 6) (y - 6)}{y^{2} - 49} \cdot \frac{y + 7}{y + 6}$

Step 3

Simplify the denominator.

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Step 3.1

Rewrite $49$ as $7^{2}$ .

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

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 $b = 7$ .

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

Step 4

Cancel the common factor of $y + 6$ .

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Step 4.1

Cancel the common factor.

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

Step 4.2

Rewrite the expression.

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

Step 5

Cancel the common factor of $y + 7$ .

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Step 5.1

Cancel the common factor.

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

Step 5.2

Rewrite the expression.

$\frac{y - 6}{y - 7}$