Basic Math Examples

$\frac{9 y + 9}{2 y^{6}} \cdot \frac{y}{y^{2} - 1}$

Step 1

Factor $9$ out of $9 y + 9$ .

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Step 1.1

Factor $9$ out of $9 y$ .

$\frac{9 (y) + 9}{2 y^{6}} \cdot \frac{y}{y^{2} - 1}$

Step 1.2

Factor $9$ out of $9$ .

$\frac{9 (y) + 9 (1)}{2 y^{6}} \cdot \frac{y}{y^{2} - 1}$

Step 1.3

Factor $9$ out of $9 (y) + 9 (1)$ .

$\frac{9 (y + 1)}{2 y^{6}} \cdot \frac{y}{y^{2} - 1}$

Step 2

Simplify the denominator.

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Step 2.1

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

$\frac{9 (y + 1)}{2 y^{6}} \cdot \frac{y}{y^{2} - 1^{2}}$

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 $b = 1$ .

$\frac{9 (y + 1)}{2 y^{6}} \cdot \frac{y}{(y + 1) (y - 1)}$

Step 3

Simplify terms.

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Step 3.1

Combine.

$\frac{9 (y + 1) y}{2 y^{6} ((y + 1) (y - 1))}$

Step 3.2

Cancel the common factor of $y + 1$ .

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Step 3.2.1

Cancel the common factor.

$\frac{9 (y + 1) y}{2 y^{6} ((y + 1) (y - 1))}$

Step 3.2.2

Rewrite the expression.

$\frac{9 y}{2 y^{6} (y - 1)}$

Step 3.3

Cancel the common factor of $y$ and $y^{6}$ .

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Step 3.3.1

Factor $y$ out of $9 y$ .

$\frac{y \cdot 9}{2 y^{6} (y - 1)}$

Step 3.3.2

Cancel the common factors.

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Step 3.3.2.1

Factor $y$ out of $2 y^{6} (y - 1)$ .

$\frac{y \cdot 9}{y (2 y^{5} (y - 1))}$

Step 3.3.2.2

Cancel the common factor.

$\frac{y \cdot 9}{y (2 y^{5} (y - 1))}$

Step 3.3.2.3

Rewrite the expression.

$\frac{9}{2 y^{5} (y - 1)}$