Solve D=2x^5-x^2/2x-x^-2

$$D = \frac { 2 x ^ { 5 } - x ^ { 2 } } { 2 x - x ^ { - 2 } }$$

Solve for D

$$D=x^{4}$$

$$x\neq \frac{2^{\frac{2}{3}}}{2}\text{ and }x\neq 0$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{2x^{5}-x^{2}}{2x-x^{-2}}.

$$D=\frac{x^{2}\left(2x^{3}-1\right)}{x^{-2}\left(2x^{3}-1\right)}$$

Cancel out 2x^{3}-1 in both numerator and denominator.

$$D=\frac{x^{2}}{x^{-2}}$$

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

$$D=x^{4}$$

Solve for x

$$\left\{\begin{matrix}x=-\sqrt[4]{D}\text{, }&D>0\\x=\sqrt[4]{D}\text{, }&D\neq \frac{2^{\frac{2}{3}}}{4}\text{ and }D>0\end{matrix}\right.$$