Precalculus Examples

$\frac{2 + \frac{4}{y^{2}}}{\frac{3}{y} - 5}$

Step 1

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

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Step 1.1

Multiply $\frac{2 + \frac{4}{y^{2}}}{\frac{3}{y} - 5}$ by $\frac{y^{2}}{y^{2}}$ .

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

Step 1.2

Combine.

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

Step 2

Apply the distributive property.

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

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

Cancel the common factor.

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

Step 3.1.2

Rewrite the expression.

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

Step 3.2

Cancel the common factor of $y$ .

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Step 3.2.1

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

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 4

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

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Step 4.1

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

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

Step 4.2

Factor $2$ out of $4$ .

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

Step 4.3

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

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

Step 5

Simplify the denominator.

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Step 5.1

Factor $y$ out of $y \cdot 3 + y^{2} \cdot - 5$ .

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Step 5.1.1

Factor $y$ out of $y \cdot 3$ .

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

Step 5.1.2

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

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

Step 5.1.3

Factor $y$ out of $y (3) + y (y \cdot - 5)$ .

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

Step 5.2

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

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