Basic Math Examples

$\frac{13 y - 13}{y^{2} - 1}$

Step 1

Factor $13$ out of $13 y - 13$ .

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Step 1.1

Factor $13$ out of $13 y$ .

$\frac{13 (y) - 13}{y^{2} - 1}$

Step 1.2

Factor $13$ out of $- 13$ .

$\frac{13 (y) + 13 (- 1)}{y^{2} - 1}$

Step 1.3

Factor $13$ out of $13 (y) + 13 (- 1)$ .

$\frac{13 (y - 1)}{y^{2} - 1}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $1$ as $1^{2}$ .

$\frac{13 (y - 1)}{y^{2} - 1^{2}}$

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 $b = 1$ .

$\frac{13 (y - 1)}{(y + 1) (y - 1)}$

Step 3

Cancel the common factor of $y - 1$ .

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Step 3.1

Cancel the common factor.

$\frac{13 (y - 1)}{(y + 1) (y - 1)}$

Step 3.2

Rewrite the expression.

$\frac{13}{y + 1}$