Simplify (4/(x+1)+2/x)/(2/(x+1))

$\frac{\frac{4}{x + 1} + \frac{2}{x}}{\frac{2}{x + 1}}$

Multiply the numerator by the reciprocal of the denominator.

$(\frac{4}{x + 1} + \frac{2}{x}) \frac{x + 1}{2}$

To write $\frac{4}{x + 1}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$(\frac{4}{x + 1} \cdot \frac{x}{x} + \frac{2}{x}) \frac{x + 1}{2}$

To write $\frac{2}{x}$ as a fraction with a common denominator, multiply by $\frac{x + 1}{x + 1}$ .

$(\frac{4}{x + 1} \cdot \frac{x}{x} + \frac{2}{x} \cdot \frac{x + 1}{x + 1}) \frac{x + 1}{2}$

Write each expression with a common denominator of $(x + 1) x$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{4}{x + 1}$ by $\frac{x}{x}$ .

$(\frac{4 x}{(x + 1) x} + \frac{2}{x} \cdot \frac{x + 1}{x + 1}) \frac{x + 1}{2}$

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

$(\frac{4 x}{(x + 1) x} + \frac{2 (x + 1)}{x (x + 1)}) \frac{x + 1}{2}$

Reorder the factors of $(x + 1) x$ .

$(\frac{4 x}{x (x + 1)} + \frac{2 (x + 1)}{x (x + 1)}) \frac{x + 1}{2}$

Combine the numerators over the common denominator.

$\frac{4 x + 2 (x + 1)}{x (x + 1)} \cdot \frac{x + 1}{2}$

Simplify the numerator.

Factor $2$ out of $4 x + 2 (x + 1)$ .

Factor $2$ out of $4 x$ .

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

Factor $2$ out of $2 (2 x) + 2 (x + 1)$ .

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

Add $2 x$ and $x$ .

$\frac{2 (3 x + 1)}{x (x + 1)} \cdot \frac{x + 1}{2}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 (3 x + 1)}{x (x + 1)} \cdot \frac{x + 1}{2}$

Rewrite the expression.

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

Cancel the common factor of $x + 1$ .

Factor $x + 1$ out of $x (x + 1)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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