Precalculus Examples

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

Step 1

Multiply the numerator by the reciprocal of the denominator.

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

Step 2

Simplify the denominator.

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Step 2.1

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

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

Step 2.2

Combine the numerators over the common denominator.

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

Step 2.3

Add $x$ and $x$ .

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

Step 3

Multiply the numerator by the reciprocal of the denominator.

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

Step 4

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

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

Step 5

Cancel the common factor of $x + 1$ .

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Step 5.1

Cancel the common factor.

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

Step 5.2

Rewrite the expression.

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

Step 6

Combine $x$ and $\frac{1}{2 x + 1}$ .

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