Algebra Examples

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

Step 1

Multiply the numerator by the reciprocal of the denominator.

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

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $2 y^{2}$ .

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Step 2.1.1

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

$\frac{y + 2}{2 y^{2} (2)} \cdot \frac{2 y^{3}}{3 y + 6}$

Step 2.1.2

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

$\frac{y + 2}{2 y^{2} (2)} \cdot \frac{2 y^{2} (y)}{3 y + 6}$

Step 2.1.3

Cancel the common factor.

$\frac{y + 2}{2 y^{2} \cdot 2} \cdot \frac{2 y^{2} y}{3 y + 6}$

Step 2.1.4

Rewrite the expression.

$\frac{y + 2}{2} \cdot \frac{y}{3 y + 6}$

Step 2.2

Multiply $\frac{y + 2}{2}$ by $\frac{y}{3 y + 6}$ .

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

Step 3

Simplify the denominator.

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Step 3.1

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

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Step 3.1.1

Factor $3$ out of $3 y$ .

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

Step 3.1.2

Factor $3$ out of $6$ .

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

Step 3.1.3

Factor $3$ out of $3 y + 3 \cdot 2$ .

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

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

Step 3.2

Multiply $2$ by $3$ .

$\frac{(y + 2) y}{6 (y + 2)}$

Step 4

Cancel the common factor of $y + 2$ .

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Step 4.1

Cancel the common factor.

$\frac{(y + 2) y}{6 (y + 2)}$

Step 4.2

Rewrite the expression.

$\frac{y}{6}$