Question

(x\sqrt(x)-8)/(x+2\sqrt(x)+4)+3(1-\sqrt(x))

Answer 1

\(\dfrac{x\sqrt{x}-8}{x+2\sqrt{x}+4}+3\left(1-\sqrt{x}\right)\)

\(=\dfrac{\left(\sqrt{x}-2\right)\left(x+2\sqrt{x}+4\right)}{x+2\sqrt{x}+4}+3-3\sqrt{x}\)

\(=\sqrt{x}-2+3-3\sqrt{x}=-2\sqrt{x}+1\)

Answer 2

\(\dfrac{x\sqrt{x}-8}{x+2\sqrt{x}+4}+3\left(1-\sqrt{x}\right)\)

\(=\dfrac{\left(\sqrt{x}\right)^3-2^3}{x+2\sqrt{x}+4}+3\left(1-\sqrt{x}\right)\)

\(=\dfrac{\left(\sqrt{x}-2\right)\left(x+2\sqrt{x}+4\right)}{x+2\sqrt{x}+4}+3-3\sqrt{x}\)

\(=\sqrt{x}-2+3-3\sqrt{x}\)

\(=\left(1-3\right)\sqrt{x}+\left(-2+3\right)\)

\(=-2\sqrt{x}+1\)