Solve 2sqrt{x+4}+2x^2-10x+8x-40/2sqrt{x+4}

$$2 \sqrt{ x+4 } + \frac{ 2 { x }^{ 2 } -10x+8x-40 }{ 2 \sqrt{ x+4 } }$$

Factor

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

Solution Steps

Combine -10x and 8x to get -2x.

$$factor(2\sqrt{x+4}+\frac{2x^{2}-2x-40}{2\sqrt{x+4}})$$

Factor the expressions that are not already factored in \frac{2x^{2}-2x-40}{2\sqrt{x+4}}.

$$factor(2\sqrt{x+4}+\frac{2\left(x-5\right)\left(x+4\right)}{2\sqrt{x+4}})$$

Cancel out 2\sqrt{x+4} in both numerator and denominator.

$$factor(2\sqrt{x+4}+\sqrt{x+4}\left(x-5\right))$$

Expand the expression.

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

Combine 2\sqrt{x+4} and -5\sqrt{x+4} to get -3\sqrt{x+4}.

$$factor(-3\sqrt{x+4}+\sqrt{x+4}x)$$

Factor out \sqrt{x+4}.

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

Evaluate

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