Solve x^frac{1{2}}(x^frac{1{2}}+x^-frac{1{2}})

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

Evaluate

$$x+1$$

Solution Steps

Use the distributive property to multiply x^{\frac{1}{2}} by x^{\frac{1}{2}}+x^{-\frac{1}{2}}.

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

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

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

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

$$x^{1}+1$$

Calculate x to the power of 1 and get x.

$$x+1$$

Factor

$$x+1$$