Solve 1+x^-1/1+x^-2

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

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored.

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

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

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

Expand the expression.

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

Expand

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

Short Solution Steps

Factor the expressions that are not already factored.

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

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

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

Expand the expression.

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