Precalculus Examples

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

Step 1

Simplify terms.

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Step 1.1

Simplify each term.

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Step 1.1.1

Simplify the denominator.

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Step 1.1.1.1

Write $1$ as a fraction with a common denominator.

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

Step 1.1.1.2

Combine the numerators over the common denominator.

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

Step 1.1.1.3

Reorder terms.

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

Step 1.1.1.4

Add $1$ and $1$ .

$1 + \frac{1}{\frac{x + 2}{x + 1}}$

Step 1.1.2

Multiply the numerator by the reciprocal of the denominator.

$1 + 1 \frac{x + 1}{x + 2}$

Step 1.1.3

Multiply $\frac{x + 1}{x + 2}$ by $1$ .

$1 + \frac{x + 1}{x + 2}$

Step 1.2

Combine into one fraction.

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Step 1.2.1

Write $1$ as a fraction with a common denominator.

$\frac{x + 2}{x + 2} + \frac{x + 1}{x + 2}$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{x + 2 + x + 1}{x + 2}$

Step 2

Simplify the numerator.

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Step 2.1

Add $x$ and $x$ .

$\frac{2 x + 2 + 1}{x + 2}$

Step 2.2

Add $2$ and $1$ .

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