Solve x-1/2x^-frac{3{2}}+1/2x^-frac{3{2}}-1/2x^-frac{1{2}}

$$\frac { x - 1 } { 2 } x ^ { - \frac { 3 } { 2 } } + \frac { 1 } { 2 } x ^ { - \frac { 3 } { 2 } } - \frac { 1 } { 2 } x ^ { - \frac { 1 } { 2 } }$$

Factor

$$0$$

Solution Steps

Factor out \frac{1}{2}.

$$\frac{\frac{x-1}{x^{\frac{3}{2}}}+\frac{1}{x^{\frac{3}{2}}}-\frac{1}{\sqrt{x}}}{2}$$

Consider \left(x-1\right)x^{-\frac{3}{2}}+x^{-\frac{3}{2}}-x^{-\frac{1}{2}}. Factor out \frac{1}{\sqrt{x}}.

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

Rewrite the complete factored expression.

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

Evaluate

$$0$$