Question

mn giúp mk vs

Answer 1

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

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

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

\(=\dfrac{2}{x+\sqrt{x}+1}\)

b: Ta có: \(x=\dfrac{8}{\sqrt{5}-1}-\dfrac{8}{\sqrt{5}+1}\)

\(=2\left(\sqrt{5}+1\right)-2\left(\sqrt{5}-1\right)\)

\(=2\sqrt{5}+2-2\sqrt{5}+2\)

=4

Thay x=4 vào M, ta được:

\(M=\dfrac{2}{4+2+1}=\dfrac{2}{7}\)