Question

Rút gọn M= \(\dfrac{-3\left(3\sqrt{x}+1\right)}{x-9}+\dfrac{2+\sqrt{x}}{\sqrt{x}-3}-\dfrac{\sqrt{x}-2}{\sqrt{x}+3}\)

Answer 1

ĐK : \(x\ge0;x\ne9\)

\(M=\dfrac{-3\left(3\sqrt{x}+1\right)}{x-9}+\dfrac{2+\sqrt{x}}{\sqrt{x}-3}-\dfrac{\sqrt{x}-2}{\sqrt{x}+3}\)

\(=\dfrac{-9\sqrt{x}-3}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}+\dfrac{\left(\sqrt{x}+2\right)\left(\sqrt{x}+3\right)}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}-\dfrac{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}\)

\(=\dfrac{-9\sqrt{x}-3+x+5\sqrt{x}+6-x+5\sqrt{x}-6}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}\)

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