Basic Math Examples

$\frac{\frac{1}{y^{2}} + \frac{2}{3}}{\frac{1}{y} - \frac{5}{6}}$

Step 1

Multiply the numerator and denominator of the fraction by $6 y^{2}$ .

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Step 1.1

Multiply $\frac{\frac{1}{y^{2}} + \frac{2}{3}}{\frac{1}{y} - \frac{5}{6}}$ by $\frac{6 y^{2}}{6 y^{2}}$ .

$\frac{6 y^{2}}{6 y^{2}} \cdot \frac{\frac{1}{y^{2}} + \frac{2}{3}}{\frac{1}{y} - \frac{5}{6}}$

Step 1.2

Combine.

$\frac{6 y^{2} (\frac{1}{y^{2}} + \frac{2}{3})}{6 y^{2} (\frac{1}{y} - \frac{5}{6})}$

Step 2

Apply the distributive property.

$\frac{6 y^{2} \frac{1}{y^{2}} + 6 y^{2} \frac{2}{3}}{6 y^{2} \frac{1}{y} + 6 y^{2} (- \frac{5}{6})}$

Step 3

Simplify by cancelling.

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Step 3.1

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

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Step 3.1.1

Factor $y^{2}$ out of $6 y^{2}$ .

$\frac{y^{2} \cdot 6 \frac{1}{y^{2}} + 6 y^{2} \frac{2}{3}}{6 y^{2} \frac{1}{y} + 6 y^{2} (- \frac{5}{6})}$

Step 3.1.2

Cancel the common factor.

$\frac{y^{2} \cdot 6 \frac{1}{y^{2}} + 6 y^{2} \frac{2}{3}}{6 y^{2} \frac{1}{y} + 6 y^{2} (- \frac{5}{6})}$

Step 3.1.3

Rewrite the expression.

$\frac{6 + 6 y^{2} \frac{2}{3}}{6 y^{2} \frac{1}{y} + 6 y^{2} (- \frac{5}{6})}$

Step 3.2

Cancel the common factor of $3$ .

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Step 3.2.1

Factor $3$ out of $6 y^{2}$ .

$\frac{6 + 3 (2 y^{2}) \frac{2}{3}}{6 y^{2} \frac{1}{y} + 6 y^{2} (- \frac{5}{6})}$

Step 3.2.2

Cancel the common factor.

$\frac{6 + 3 (2 y^{2}) \frac{2}{3}}{6 y^{2} \frac{1}{y} + 6 y^{2} (- \frac{5}{6})}$

Step 3.2.3

Rewrite the expression.

$\frac{6 + 2 y^{2} \cdot 2}{6 y^{2} \frac{1}{y} + 6 y^{2} (- \frac{5}{6})}$

Step 3.3

Multiply $2$ by $2$ .

$\frac{6 + 4 y^{2}}{6 y^{2} \frac{1}{y} + 6 y^{2} (- \frac{5}{6})}$

Step 3.4

Cancel the common factor of $y$ .

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Step 3.4.1

Factor $y$ out of $6 y^{2}$ .

$\frac{6 + 4 y^{2}}{y (6 y) \frac{1}{y} + 6 y^{2} (- \frac{5}{6})}$

Step 3.4.2

Cancel the common factor.

$\frac{6 + 4 y^{2}}{y (6 y) \frac{1}{y} + 6 y^{2} (- \frac{5}{6})}$

Step 3.4.3

Rewrite the expression.

$\frac{6 + 4 y^{2}}{6 y + 6 y^{2} (- \frac{5}{6})}$

Step 3.5

Cancel the common factor of $6$ .

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Step 3.5.1

Move the leading negative in $- \frac{5}{6}$ into the numerator.

$\frac{6 + 4 y^{2}}{6 y + 6 y^{2} \frac{- 5}{6}}$

Step 3.5.2

Factor $6$ out of $6 y^{2}$ .

$\frac{6 + 4 y^{2}}{6 y + 6 (y^{2}) \frac{- 5}{6}}$

Step 3.5.3

Cancel the common factor.

$\frac{6 + 4 y^{2}}{6 y + 6 y^{2} \frac{- 5}{6}}$

Step 3.5.4

Rewrite the expression.

$\frac{6 + 4 y^{2}}{6 y + y^{2} \cdot - 5}$

Step 4

Factor $2$ out of $6 + 4 y^{2}$ .

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Step 4.1

Factor $2$ out of $6$ .

$\frac{2 (3) + 4 y^{2}}{6 y + y^{2} \cdot - 5}$

Step 4.2

Factor $2$ out of $4 y^{2}$ .

$\frac{2 (3) + 2 (2 y^{2})}{6 y + y^{2} \cdot - 5}$

Step 4.3

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

$\frac{2 (3 + 2 y^{2})}{6 y + y^{2} \cdot - 5}$

Step 5

Simplify the denominator.

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Step 5.1

Factor $y$ out of $6 y + y^{2} \cdot - 5$ .

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Step 5.1.1

Factor $y$ out of $6 y$ .

$\frac{2 (3 + 2 y^{2})}{y \cdot 6 + y^{2} \cdot - 5}$

Step 5.1.2

Factor $y$ out of $y^{2} \cdot - 5$ .

$\frac{2 (3 + 2 y^{2})}{y \cdot 6 + y (y \cdot - 5)}$

Step 5.1.3

Factor $y$ out of $y \cdot 6 + y (y \cdot - 5)$ .

$\frac{2 (3 + 2 y^{2})}{y (6 + y \cdot - 5)}$

Step 5.2

Move $- 5$ to the left of $y$ .

$\frac{2 (3 + 2 y^{2})}{y (6 - 5 y)}$