Solve x^3-x^5/2*x^2/x^1/2=

$$\frac { x ^ { 3 } - x ^ { 5 / 2 } \cdot x ^ { 2 } } { x ^ { 1 / 2 } } =$$

Evaluate

$$x^{\frac{5}{2}}-x^{4}$$

Short Solution Steps

To multiply powers of the same base, add their exponents. Add \frac{5}{2} and 2 to get \frac{9}{2}.

$$\frac{x^{3}-x^{\frac{9}{2}}}{x^{\frac{1}{2}}}$$

Factor the expressions that are not already factored.

$$\frac{\left(-x^{\frac{3}{2}}+1\right)x^{3}}{\sqrt{x}}$$

Cancel out \sqrt{x} in both numerator and denominator.

$$\left(-x^{\frac{3}{2}}+1\right)x^{\frac{5}{2}}$$

Expand the expression.

$$-x^{4}+x^{\frac{5}{2}}$$

Factor

$$\left(1-x^{\frac{3}{2}}\right)x^{\frac{5}{2}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add \frac{5}{2} and 2 to get \frac{9}{2}.

$$factor(\frac{x^{3}-x^{\frac{9}{2}}}{x^{\frac{1}{2}}})$$

Factor the expressions that are not already factored in \frac{x^{3}-x^{\frac{9}{2}}}{x^{\frac{1}{2}}}.

$$factor(\frac{\left(-x^{\frac{3}{2}}+1\right)x^{3}}{\sqrt{x}})$$

Cancel out \sqrt{x} in both numerator and denominator.

$$factor(\left(-x^{\frac{3}{2}}+1\right)x^{\frac{5}{2}})$$

Expand the expression.

$$factor(-x^{4}+x^{\frac{5}{2}})$$

Factor out x^{\frac{5}{2}}.

$$x^{\frac{5}{2}}\left(-x^{\frac{3}{2}}+1\right)$$