Precalculus Examples

$\frac{1}{(\frac{1}{x + 3}) + 3}$

Step 1

Simplify the denominator.

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Step 1.1

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

$\frac{1}{\frac{1}{x + 3} + \frac{3 (x + 3)}{x + 3}}$

Step 1.2

Combine the numerators over the common denominator.

$\frac{1}{\frac{1 + 3 (x + 3)}{x + 3}}$

Step 1.3

Reorder terms.

$\frac{1}{\frac{3 (x + 3) + 1}{x + 3}}$

Step 1.4

Rewrite $\frac{3 (x + 3) + 1}{x + 3}$ in a factored form.

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Step 1.4.1

Apply the distributive property.

$\frac{1}{\frac{3 x + 3 \cdot 3 + 1}{x + 3}}$

Step 1.4.2

Multiply $3$ by $3$ .

$\frac{1}{\frac{3 x + 9 + 1}{x + 3}}$

Step 1.4.3

Add $9$ and $1$ .

$\frac{1}{\frac{3 x + 10}{x + 3}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$1 \frac{x + 3}{3 x + 10}$

Step 3

Multiply $\frac{x + 3}{3 x + 10}$ by $1$ .

$\frac{x + 3}{3 x + 10}$