Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

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

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

Step 1.1.2

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

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

Step 1.1.3

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

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

Step 1.2

Cancel the common factor of $y$ .

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Step 1.2.1

Cancel the common factor.

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

Step 1.2.2

Rewrite the expression.

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

Step 2

To write $- \frac{1}{y + 2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 3

Write each expression with a common denominator of $3 (y + 2)$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{1}{y + 2}$ by $\frac{3}{3}$ .

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

Step 3.2

Reorder the factors of $(y + 2) \cdot 3$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Subtract $3$ from $4$ .

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