Pre-Algebra Examples

$\frac{3 y - 1}{y^{2} + 4 y} + \frac{9 y + 6}{y (y + 4)}$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

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

$\frac{3 y - 1}{y \cdot y + 4 y} + \frac{9 y + 6}{y (y + 4)}$

Step 1.1.2

Factor $y$ out of $4 y$ .

$\frac{3 y - 1}{y \cdot y + y \cdot 4} + \frac{9 y + 6}{y (y + 4)}$

Step 1.1.3

Factor $y$ out of $y \cdot y + y \cdot 4$ .

$\frac{3 y - 1}{y (y + 4)} + \frac{9 y + 6}{y (y + 4)}$

Step 1.2

Factor $3$ out of $9 y + 6$ .

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Step 1.2.1

Factor $3$ out of $9 y$ .

$\frac{3 y - 1}{y (y + 4)} + \frac{3 (3 y) + 6}{y (y + 4)}$

Step 1.2.2

Factor $3$ out of $6$ .

$\frac{3 y - 1}{y (y + 4)} + \frac{3 (3 y) + 3 (2)}{y (y + 4)}$

Step 1.2.3

Factor $3$ out of $3 (3 y) + 3 (2)$ .

$\frac{3 y - 1}{y (y + 4)} + \frac{3 (3 y + 2)}{y (y + 4)}$

Step 2

Combine the numerators over the common denominator.

$\frac{3 y - 1 + 3 (3 y + 2)}{y (y + 4)}$

Step 3

Simplify the numerator.

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Step 3.1

Simplify each term.

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Step 3.1.1

Apply the distributive property.

$\frac{3 y - 1 + 3 (3 y) + 3 \cdot 2}{y (y + 4)}$

Step 3.1.2

Multiply $3$ by $3$ .

$\frac{3 y - 1 + 9 y + 3 \cdot 2}{y (y + 4)}$

Step 3.1.3

Multiply $3$ by $2$ .

$\frac{3 y - 1 + 9 y + 6}{y (y + 4)}$

Step 3.2

Add $3 y$ and $9 y$ .

$\frac{12 y - 1 + 6}{y (y + 4)}$

Step 3.3

Add $- 1$ and $6$ .

$\frac{12 y + 5}{y (y + 4)}$