Question

Rút gọn biểu thức : \(x\sqrt{2x+2}+\left(x+1\right)\sqrt{\dfrac{2}{x+1}}-4\sqrt{\dfrac{x+1}{2}}\)

Answer 1

ĐK: \(x>-1\)

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

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

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

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

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