Solve 2xsqrt{x}-4sqrt{x}+x^2-4x/2sqrt{x}

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

Factor

$$\frac{\sqrt{x}\left(5x-12\right)}{2}$$

Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-4x}{2\sqrt{x}}.

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

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

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

Use the distributive property to multiply \sqrt{x} by x-4.

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

Factor out \frac{1}{2}.

$$\frac{4x\sqrt{x}-8\sqrt{x}+\sqrt{x}x-4\sqrt{x}}{2}$$

Consider 4x^{\frac{3}{2}}-8\sqrt{x}+x^{\frac{3}{2}}-4\sqrt{x}. Factor out \sqrt{x}.

$$\sqrt{x}\left(5x-12\right)$$

Consider 4x-8+x-4. Multiply and combine like terms.

$$5x-12$$

Rewrite the complete factored expression.

$$\frac{\sqrt{x}\left(5x-12\right)}{2}$$

Evaluate

$$\frac{\sqrt{x}\left(5x-12\right)}{2}$$