Precalculus Examples

$\frac{y^{2} + 3 y}{y^{3} + 3 y^{2} - 5 y - 15}$

Step 1

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

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Step 1.1

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

$\frac{y \cdot y + 3 y}{y^{3} + 3 y^{2} - 5 y - 15}$

Step 1.2

Factor $y$ out of $3 y$ .

$\frac{y \cdot y + y \cdot 3}{y^{3} + 3 y^{2} - 5 y - 15}$

Step 1.3

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

$\frac{y (y + 3)}{y^{3} + 3 y^{2} - 5 y - 15}$

Step 2

Simplify the denominator.

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Step 2.1

Factor out the greatest common factor from each group.

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Step 2.1.1

Group the first two terms and the last two terms.

$\frac{y (y + 3)}{(y^{3} + 3 y^{2}) - 5 y - 15}$

Step 2.1.2

Factor out the greatest common factor (GCF) from each group.

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

Step 2.2

Factor the polynomial by factoring out the greatest common factor, $y + 3$ .

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

Step 3

Cancel the common factor of $y + 3$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

$\frac{y}{y^{2} - 5}$