Basic Math Examples

$\frac{\frac{3 u + 6}{u + 5}}{\frac{u + 2}{5 u}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{3 u + 6}{u + 5} \cdot \frac{5 u}{u + 2}$

Step 2

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

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Step 2.1

Factor $3$ out of $3 u$ .

$\frac{3 (u) + 6}{u + 5} \cdot \frac{5 u}{u + 2}$

Step 2.2

Factor $3$ out of $6$ .

$\frac{3 u + 3 \cdot 2}{u + 5} \cdot \frac{5 u}{u + 2}$

Step 2.3

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

$\frac{3 (u + 2)}{u + 5} \cdot \frac{5 u}{u + 2}$

Step 3

Cancel the common factor of $u + 2$ .

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Step 3.1

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

$\frac{(u + 2) \cdot 3}{u + 5} \cdot \frac{5 u}{u + 2}$

Step 3.2

Cancel the common factor.

$\frac{(u + 2) \cdot 3}{u + 5} \cdot \frac{5 u}{u + 2}$

Step 3.3

Rewrite the expression.

$\frac{3}{u + 5} (5 u)$

Step 4

Combine $5$ and $\frac{3}{u + 5}$ .

$\frac{5 \cdot 3}{u + 5} u$

Step 5

Multiply $5$ by $3$ .

$\frac{15}{u + 5} u$

Step 6

Combine $\frac{15}{u + 5}$ and $u$ .

$\frac{15 u}{u + 5}$