Solve 3x^2-6x/2sqrt{x}+6x^frac{3{2}}-6x^frac{1{2}}

$$\frac { 3 x ^ { 2 } - 6 x } { 2 \sqrt { x } } + 6 x ^ { \frac { 3 } { 2 } } - 6 x ^ { \frac { 1 } { 2 } }$$

Factor

$$\frac{3\sqrt{x}\left(5x-6\right)}{2}$$

Solution Steps

Factor the expressions that are not already factored in \frac{3x^{2}-6x}{2\sqrt{x}}.

$$factor(\frac{3x\left(x-2\right)}{2\sqrt{x}}+6x^{\frac{3}{2}}-6x^{\frac{1}{2}})$$

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

$$factor(\frac{3\sqrt{x}\left(x-2\right)}{2}+6x^{\frac{3}{2}}-6x^{\frac{1}{2}})$$

Use the distributive property to multiply 3\sqrt{x} by x-2.

$$factor(\frac{3\sqrt{x}x-6\sqrt{x}}{2}+6x^{\frac{3}{2}}-6x^{\frac{1}{2}})$$

Factor out \frac{3}{2}.

$$\frac{3\left(\sqrt{x}x-2\sqrt{x}+4x^{\frac{3}{2}}-4\sqrt{x}\right)}{2}$$

Consider x^{\frac{3}{2}}-2\sqrt{x}+4x^{\frac{3}{2}}-4\sqrt{x}. Factor out \sqrt{x}.

$$\sqrt{x}\left(5x-6\right)$$

Consider x-2+4x-4. Multiply and combine like terms.

$$5x-6$$

Rewrite the complete factored expression.

$$\frac{3\sqrt{x}\left(5x-6\right)}{2}$$

Evaluate

$$\frac{3\sqrt{x}\left(5x-6\right)}{2}$$