Solve 2xsqrt{x}-3sqrt{x^3}+x/5sqrt{x^5}

$$2 x \sqrt { x } - 3 \sqrt { x ^ { 3 } } + \frac { x } { 5 } \sqrt { x ^ { 5 } }$$

Factor

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

Solution Steps

Factor out \frac{1}{5}.

$$\frac{10x\sqrt{x}-15x^{\frac{3}{2}}+xx^{\frac{5}{2}}}{5}$$

Consider 10x^{\frac{3}{2}}-15x^{\frac{3}{2}}+x^{\frac{7}{2}}. Factor out x^{\frac{3}{2}}.

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

Rewrite the complete factored expression. Polynomial x^{2}-5 is not factored since it does not have any rational roots.

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

Evaluate

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