Algebra Examples

$\frac{3 x}{16} \div \frac{3 x - 9}{20}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{3 x}{16} \cdot \frac{20}{3 x - 9}$

Step 2

Cancel the common factor of $4$ .

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Step 2.1

Factor $4$ out of $16$ .

$\frac{3 x}{4 (4)} \cdot \frac{20}{3 x - 9}$

Step 2.2

Factor $4$ out of $20$ .

$\frac{3 x}{4 \cdot 4} \cdot \frac{4 \cdot 5}{3 x - 9}$

Step 2.3

Cancel the common factor.

$\frac{3 x}{4 \cdot 4} \cdot \frac{4 \cdot 5}{3 x - 9}$

Step 2.4

Rewrite the expression.

$\frac{3 x}{4} \cdot \frac{5}{3 x - 9}$

Step 3

Multiply $\frac{3 x}{4}$ by $\frac{5}{3 x - 9}$ .

$\frac{3 x \cdot 5}{4 (3 x - 9)}$

Step 4

Multiply $5$ by $3$ .

$\frac{15 x}{4 (3 x - 9)}$

Step 5

Cancel the common factor of $15$ and $3 x - 9$ .

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Step 5.1

Factor $3$ out of $15 x$ .

$\frac{3 (5 x)}{4 (3 x - 9)}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $3$ out of $4 (3 x - 9)$ .

$\frac{3 (5 x)}{3 (4 (x - 3))}$

Step 5.2.2

Cancel the common factor.

$\frac{3 (5 x)}{3 (4 (x - 3))}$

Step 5.2.3

Rewrite the expression.

$\frac{5 x}{4 (x - 3)}$