Simplify (x/(x+1)+1)*(1+x)/(2x-1)

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

Step 1

Combine into one fraction.

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

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

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.

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

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

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

Reorder terms.

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

Cancel the common factor.

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

Rewrite the expression.

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