Solve (n+x)+x/1+x

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

Evaluate

$$\frac{x^{2}+nx+2x+n}{x+1}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply n+x times \frac{1+x}{1+x}.

$$\frac{\left(n+x\right)\left(1+x\right)}{1+x}+\frac{x}{1+x}$$

Since \frac{\left(n+x\right)\left(1+x\right)}{1+x} and \frac{x}{1+x} have the same denominator, add them by adding their numerators.

$$\frac{\left(n+x\right)\left(1+x\right)+x}{1+x}$$

Do the multiplications in \left(n+x\right)\left(1+x\right)+x.

$$\frac{n+nx+x+x^{2}+x}{1+x}$$

Combine like terms in n+nx+x+x^{2}+x.

$$\frac{n+x^{2}+nx+2x}{1+x}$$

Differentiate w.r.t. x

$$\frac{x^{2}+2x+2}{\left(x+1\right)^{2}}$$