Basic Math Examples

$\frac{y - 6}{y - 7} \div \frac{y + 2}{y^{2} \div 8 y + 12}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{y - 6}{y - 7} \cdot \frac{y^{2} \div 8 y + 12}{y + 2}$

Step 2

Cancel the common factor of $y^{2}$ and $y$ .

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Step 2.1

Factor $y$ out of $y^{2}$ .

$\frac{y - 6}{y - 7} \cdot \frac{y \cdot y \div 8 y + 12}{y + 2}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $y$ out of $8 y$ .

$\frac{y - 6}{y - 7} \cdot \frac{y \cdot y \div y \cdot 8 + 12}{y + 2}$

Step 2.2.2

Cancel the common factor.

$\frac{y - 6}{y - 7} \cdot \frac{y \cdot y \div y \cdot 8 + 12}{y + 2}$

Step 2.2.3

Rewrite the expression.

$\frac{y - 6}{y - 7} \cdot \frac{\frac{y}{8} + 12}{y + 2}$

Step 3

Multiply the numerator and denominator of the fraction by $8$ .

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Step 3.1

Multiply $\frac{\frac{y}{8} + 12}{y + 2}$ by $\frac{8}{8}$ .

$\frac{y - 6}{y - 7} (\frac{8}{8} \cdot \frac{\frac{y}{8} + 12}{y + 2})$

Step 3.2

Combine.

$\frac{y - 6}{y - 7} \cdot \frac{8 (\frac{y}{8} + 12)}{8 (y + 2)}$

Step 4

Apply the distributive property.

$\frac{y - 6}{y - 7} \cdot \frac{8 \frac{y}{8} + 8 \cdot 12}{8 y + 8 \cdot 2}$

Step 5

Simplify terms.

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Step 5.1

Cancel the common factor of $8$ .

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Step 5.1.1

Cancel the common factor.

$\frac{y - 6}{y - 7} \cdot \frac{8 \frac{y}{8} + 8 \cdot 12}{8 y + 8 \cdot 2}$

Step 5.1.2

Rewrite the expression.

$\frac{y - 6}{y - 7} \cdot \frac{y + 8 \cdot 12}{8 y + 8 \cdot 2}$

Step 5.2

Multiply $8$ by $12$ .

$\frac{y - 6}{y - 7} \cdot \frac{y + 96}{8 y + 8 \cdot 2}$

Step 5.3

Factor $8$ out of $8 y + 8 \cdot 2$ .

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Step 5.3.1

Factor $8$ out of $8 y$ .

$\frac{y - 6}{y - 7} \cdot \frac{y + 96}{8 (y) + 8 \cdot 2}$

Step 5.3.2

Factor $8$ out of $8 \cdot 2$ .

$\frac{y - 6}{y - 7} \cdot \frac{y + 96}{8 (y) + 8 (2)}$

Step 5.3.3

Factor $8$ out of $8 (y) + 8 (2)$ .

$\frac{y - 6}{y - 7} \cdot \frac{y + 96}{8 (y + 2)}$

Step 5.4

Multiply $\frac{y - 6}{y - 7}$ by $\frac{y + 96}{8 (y + 2)}$ .

$\frac{(y - 6) (y + 96)}{(y - 7) (8 (y + 2))}$

Step 5.5

Move $8$ to the left of $y - 7$ .

$\frac{(y - 6) (y + 96)}{8 (y - 7) (y + 2)}$