Question

\(A=\left(\dfrac{\sqrt{x}+2}{\sqrt{x}+1}-\dfrac{2\sqrt{x}-2}{\sqrt{x}-1}\right).\left(x-1\right)\)

a) Tính A khi x=4

b) Rút gọn A và tìm GTLN của A

Answer 1

a: Khi x=4 thì \(A=\left(\dfrac{2+2}{2+1}-\dfrac{2\cdot2-2}{2-1}\right)\cdot\left(4-1\right)=\dfrac{1}{3}\cdot3=1\)

b: \(A=\left(\dfrac{\sqrt{x}+2}{\sqrt{x}+1}-2\right)\cdot\left(x-1\right)\)

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