Question

mong các cậu giúp:3

Answer 1

\(ĐKXĐ:a>0,a\ne\pm1\)

Có : \(P=\left(\dfrac{\sqrt{a}}{\sqrt{a}-1}+\dfrac{\sqrt{a}}{a-\sqrt{a}}\right):\dfrac{\sqrt{a}+1}{3}\)

\(=\left(\dfrac{\sqrt{a}}{\sqrt{a}-1}+\dfrac{\sqrt{a}}{\sqrt{a}\left(\sqrt{a}-1\right)}\right):\dfrac{\sqrt{a}+1}{3}\)

\(=\left(\dfrac{\sqrt{a}}{\sqrt{a}-1}+\dfrac{1}{\sqrt{a}-1}\right):\dfrac{\sqrt{a}+1}{3}\)

\(=\dfrac{\sqrt{a}+1}{\sqrt{a}-1}\cdot\dfrac{3}{\sqrt{a}+1}=\dfrac{3}{\sqrt{a}-1}\)

Vậy \(P=\dfrac{3}{\sqrt{x}-1}\) với \(x>0,x\ne\pm1\)