Finite Math Examples

$\frac{y^{6}}{9 y + 81} \cdot \frac{6 y + 54}{6 y^{8}}$

Step 1

Factor $9$ out of $9 y + 81$ .

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Step 1.1

Factor $9$ out of $9 y$ .

$\frac{y^{6}}{9 (y) + 81} \cdot \frac{6 y + 54}{6 y^{8}}$

Step 1.2

Factor $9$ out of $81$ .

$\frac{y^{6}}{9 y + 9 \cdot 9} \cdot \frac{6 y + 54}{6 y^{8}}$

Step 1.3

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

$\frac{y^{6}}{9 (y + 9)} \cdot \frac{6 y + 54}{6 y^{8}}$

Step 2

Factor $6$ out of $6 y + 54$ .

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Step 2.1

Factor $6$ out of $6 y$ .

$\frac{y^{6}}{9 (y + 9)} \cdot \frac{6 (y) + 54}{6 y^{8}}$

Step 2.2

Factor $6$ out of $54$ .

$\frac{y^{6}}{9 (y + 9)} \cdot \frac{6 y + 6 \cdot 9}{6 y^{8}}$

Step 2.3

Factor $6$ out of $6 y + 6 \cdot 9$ .

$\frac{y^{6}}{9 (y + 9)} \cdot \frac{6 (y + 9)}{6 y^{8}}$

Step 3

Combine.

$\frac{y^{6} (6 (y + 9))}{9 (y + 9) (6 y^{8})}$

Step 4

Cancel the common factors.

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Step 4.1

Factor $y^{6}$ out of $9 (y + 9) (6 y^{8})$ .

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

Step 4.2

Cancel the common factor.

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

Step 4.3

Rewrite the expression.

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

Step 5

Cancel the common factor of $6$ and $9$ .

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Step 5.1

Factor $3$ out of $6 (y + 9)$ .

$\frac{3 (2 (y + 9))}{9 (y + 9) (6 y^{2})}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $3$ out of $9 (y + 9) (6 y^{2})$ .

$\frac{3 (2 (y + 9))}{3 (3 (y + 9) (6 y^{2}))}$

Step 5.2.2

Cancel the common factor.

$\frac{3 (2 (y + 9))}{3 (3 (y + 9) (6 y^{2}))}$

Step 5.2.3

Rewrite the expression.

$\frac{2 (y + 9)}{3 (y + 9) (6 y^{2})}$

Step 6

Cancel the common factors.

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Step 6.1

Factor $2$ out of $3 (y + 9) (6 y^{2})$ .

$\frac{2 (y + 9)}{2 (3 (y + 9) (3 y^{2}))}$

Step 6.2

Cancel the common factor.

$\frac{2 (y + 9)}{2 (3 (y + 9) (3 y^{2}))}$

Step 6.3

Rewrite the expression.

$\frac{y + 9}{3 (y + 9) (3 y^{2})}$

Step 7

Cancel the common factor of $y + 9$ .

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Step 7.1

Cancel the common factor.

$\frac{y + 9}{3 (y + 9) (3 y^{2})}$

Step 7.2

Rewrite the expression.

$\frac{1}{3 (3 y^{2})}$

Step 8

Simplify the expression.

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Step 8.1

Multiply $3$ by $3$ .

$\frac{1}{3^{2} y^{2}}$

Step 8.2

Raise $3$ to the power of $2$ .

$\frac{1}{9 y^{2}}$