Question

giải pt \(\left(\dfrac{\sqrt{a}+2}{a-4}+\sqrt{a}\right).\dfrac{\sqrt{a}-2}{\sqrt{a}-1}\) với a>0, a\(\ne\)4, a\(\ne1\)

Answer 1

\(\Leftrightarrow\left(\dfrac{\sqrt{a}+2}{\left(\sqrt{a}+2\right)\left(\sqrt{a}-2\right)}+\sqrt{a}\right).\dfrac{\sqrt{a}-2}{\sqrt{a}-1}\)

\(\Leftrightarrow\dfrac{1}{\sqrt{a}-2}+\sqrt{a}.\dfrac{\sqrt{a}-2}{\sqrt{a}-1}\)

\(\Leftrightarrow\dfrac{1+\sqrt{a}\sqrt{a}-2}{\sqrt{a}-2}.\dfrac{\sqrt{a}-2}{\sqrt{a}-1}\)

\(\Leftrightarrow\dfrac{1+a-2a}{\sqrt{a}-1}\)

\(\Leftrightarrow\dfrac{\left(\sqrt{a}-1\right)^2}{\sqrt{a}-1}\Leftrightarrow\sqrt{a}-1\)