Precalculus Examples

$\frac{9}{\frac{9}{x} + \frac{2}{3 x}}$

Step 1

Simplify the denominator.

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Step 1.1

To write $\frac{9}{x}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{9}{\frac{9}{x} \cdot \frac{3}{3} + \frac{2}{3 x}}$

Step 1.2

Write each expression with a common denominator of $x \cdot 3$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.2.1

Multiply $\frac{9}{x}$ by $\frac{3}{3}$ .

$\frac{9}{\frac{9 \cdot 3}{x \cdot 3} + \frac{2}{3 x}}$

Step 1.2.2

Move $3$ to the left of $x$ .

$\frac{9}{\frac{9 \cdot 3}{3 x} + \frac{2}{3 x}}$

Step 1.3

Combine the numerators over the common denominator.

$\frac{9}{\frac{9 \cdot 3 + 2}{3 x}}$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Multiply $9$ by $3$ .

$\frac{9}{\frac{27 + 2}{3 x}}$

Step 1.4.2

Add $27$ and $2$ .

$\frac{9}{\frac{29}{3 x}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$9 \frac{3 x}{29}$

Step 3

Multiply $9 \frac{3 x}{29}$ .

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Step 3.1

Combine $9$ and $\frac{3 x}{29}$ .

$\frac{9 (3 x)}{29}$

Step 3.2

Multiply $3$ by $9$ .

$\frac{27 x}{29}$