Question

Cho biểu thức P = \(\left(\frac{\sqrt{x}}{\sqrt{x}+1}-\frac{\sqrt{x}}{\sqrt{x}-1}\right):\frac{2}{\sqrt{x}+1}\)

a) Tìm đkxđ

b) Rút gọn

c) Tìm x để P=-2

Answer 1

đkxđ \(x\ge0,x\ne1\)

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

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

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

\(P=\frac{-\sqrt{x}}{\sqrt{x}-1}\)

để P=-1 thì

\(\frac{-\sqrt{x}}{\sqrt{x}-1}=-2< =>\sqrt{x}=2\left(\sqrt{x}-1\right)< =>\sqrt{x}=2< =>x=4\)