Question

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

a) Rút gọn M

b) Tìm x để M = \(\dfrac{\sqrt{x}+1}{\sqrt{x}+2}\)

Answer 1

\(a,M=\dfrac{x+3+2\sqrt{x}-6-\sqrt{x}-3}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}\left(x\ge0;x\ne9\right)\\ M=\dfrac{x+\sqrt{x}-6}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}=\dfrac{\left(\sqrt{x}-2\right)\left(\sqrt{x}+3\right)}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}=\dfrac{\sqrt{x}-2}{\sqrt{x}-3}\\ b,M=\dfrac{\sqrt{x}+1}{\sqrt{x}+2}\Leftrightarrow\dfrac{\sqrt{x}-2}{\sqrt{x}-3}=\dfrac{\sqrt{x}+1}{\sqrt{x}+2}\\ \Leftrightarrow x-4=x-2\sqrt{x}-3\\ \Leftrightarrow2\sqrt{x}=1\Leftrightarrow x=\dfrac{1}{4}\left(tm\right)\)