Algebra Examples

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

Step 1

Combine into one fraction.

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Step 1.1

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

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

Step 1.2

Combine the numerators over the common denominator.

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

Step 2

Add $x$ and $x$ .

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

Step 3

Simplify terms.

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Step 3.1

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

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

Step 3.2

Cancel the common factor of $1 + x$ and $x + 1$ .

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Step 3.2.1

Reorder terms.

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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