Question

\(A=\left(\dfrac{\sqrt{x}+2}{x-5\sqrt{x}+6}-\dfrac{\sqrt{x}+3}{2-\sqrt{x}}-\dfrac{\sqrt{x}+2}{\sqrt{x}-3}\right):\left(2-\dfrac{\sqrt{x}}{\sqrt{x}+1}\right)\)

a) Rút gọn A

b) Cho |x| = 3. Tính A

Answer 1

a: \(A=\dfrac{\sqrt{x}+2+x-9-x+4}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}:\dfrac{2\sqrt{x}+2-\sqrt{x}}{\sqrt{x}+1}\)

\(=\dfrac{\sqrt{x}-3}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}\cdot\dfrac{\sqrt{x}+1}{\sqrt{x}+2}=\dfrac{\sqrt{x}+1}{x-4}\)

b: |x|=3 

=>x=3(nhận) hoặc x=-3(loại)

Thay x=3 vào A, ta được:

\(A=\dfrac{\sqrt{3}+1}{3-4}=-\sqrt{3}-1\)