Precalculus Examples

$\frac{y + \frac{a^{2}}{y}}{y^{2}}$

Step 1

Simplify the numerator.

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Step 1.1

To write $y$ as a fraction with a common denominator, multiply by $\frac{y}{y}$ .

$\frac{\frac{y \cdot y}{y} + \frac{a^{2}}{y}}{y^{2}}$

Step 1.2

Combine the numerators over the common denominator.

$\frac{\frac{y \cdot y + a^{2}}{y}}{y^{2}}$

Step 1.3

Multiply $y$ by $y$ .

$\frac{\frac{y^{2} + a^{2}}{y}}{y^{2}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{y^{2} + a^{2}}{y} \cdot \frac{1}{y^{2}}$

Step 3

Multiply $\frac{y^{2} + a^{2}}{y} \cdot \frac{1}{y^{2}}$ .

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Step 3.1

Multiply $\frac{y^{2} + a^{2}}{y}$ by $\frac{1}{y^{2}}$ .

$\frac{y^{2} + a^{2}}{y \cdot y^{2}}$

Step 3.2

Multiply $y$ by $y^{2}$ by adding the exponents.

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Step 3.2.1

Multiply $y$ by $y^{2}$ .

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Step 3.2.1.1

Raise $y$ to the power of $1$ .

$\frac{y^{2} + a^{2}}{y^{1} y^{2}}$

Step 3.2.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{y^{2} + a^{2}}{y^{1 + 2}}$

Step 3.2.2

Add $1$ and $2$ .

$\frac{y^{2} + a^{2}}{y^{3}}$