Solve (1+x^-1)^2=

$$( 1 + x ^ { - 1 } ) ^ { 2 } =$$

Evaluate

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

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(1+x^{-1}\right)^{2}.

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

To raise a power to another power, multiply the exponents. Multiply -1 and 2 to get -2.

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

Expand

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

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(1+x^{-1}\right)^{2}.

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

To raise a power to another power, multiply the exponents. Multiply -1 and 2 to get -2.

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