Solve frac{x^frac{1{2}}-x^frac{9{2}}}{x^frac{7{2}}+x^-frac{1{2}}}

$$\frac { x ^ { \frac { 1 } { 2 } } - x ^ { \frac { 9 } { 2 } } } { x ^ { \frac { 7 } { 2 } } + x ^ { - \frac { 1 } { 2 } } }$$

Evaluate

$$\frac{x\left(1-x^{4}\right)}{x^{4}+1}$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{\sqrt{x}\left(x-1\right)\left(x+1\right)\left(-x^{2}-1\right)}{x^{-\frac{1}{2}}\left(x^{4}+1\right)}$$

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

$$\frac{x^{1}\left(x-1\right)\left(x+1\right)\left(-x^{2}-1\right)}{x^{4}+1}$$

Expand the expression.

$$\frac{-x^{5}+x}{x^{4}+1}$$

Factor

$$\frac{x\left(x-1\right)\left(x+1\right)\left(-x^{2}-1\right)}{x^{4}+1}$$