Solve 1+1/1+x1/x

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

Evaluate

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

Short Solution Steps

Multiply \frac{1}{1+x} times \frac{1}{x} by multiplying numerator times numerator and denominator times denominator.

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

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

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

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

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

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

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

Expand \left(1+x\right)x.

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

Differentiate w.r.t. x

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