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

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

Evaluate

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

Solution Steps

Multiply x^{\frac{1}{2}}+x^{-\frac{1}{2}} and x^{\frac{1}{2}}+x^{-\frac{1}{2}} to get \left(x^{\frac{1}{2}}+x^{-\frac{1}{2}}\right)^{2}.

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

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

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

To raise a power to another power, multiply the exponents. Multiply \frac{1}{2} and 2 to get 1.

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

Multiply x^{\frac{1}{2}} and x^{-\frac{1}{2}} to get 1.

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

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

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

Calculate x to the power of 1 and get x.

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

Factor

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