Question

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

a) rút gọn

Answer 1

Lời giải:

ĐK: \(x>0; x\neq 4\)

\(P=\left(\frac{\sqrt{x}}{\sqrt{x}-2}+\frac{4x}{2\sqrt{x}-x}\right): \frac{\sqrt{x}+3}{\sqrt{x}-2}\)

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

\(=\frac{x-4x}{\sqrt{x}(\sqrt{x}-2)}.\frac{\sqrt{x}-2}{\sqrt{x}+3}\)

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