Question

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

a rút gọn M

b, Tính M với \(x=\dfrac{2}{2-\sqrt{3}}\)

Answer 1

a , Ta có :

\(M=\left(\dfrac{\sqrt{x}+\sqrt{x}}{\sqrt{x}-1}\right):\left[\dfrac{2\left(\sqrt{x}+1\right)}{x\left(\sqrt{x}+1\right)}+\dfrac{x-2}{x\left(\sqrt{x}+1\right)}\right]\)

\(M=\dfrac{2\sqrt{x}}{\sqrt{x}-1}:\left[\dfrac{2\sqrt{x}+2+x-2}{x\left(\sqrt{x}+1\right)}\right]\)

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

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

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

b , thay vào rồi tính nhé .

Answer 2

giúp mk với