Question

Answer 1

4.1: ĐKXĐ: a>0; a<>1

\(Q=\left(\frac{1}{\sqrt{a}+1}-\frac{1}{a+\sqrt{a}}\right):\frac{\sqrt{a}-1}{a+2\sqrt{a}+1}\)

\(=\left(\frac{1}{\sqrt{a}+1}-\frac{1}{\sqrt{a}\left(\sqrt{a}+1\right)}\right)\cdot\frac{\left(\sqrt{a}+1\right)^2}{\sqrt{a}-1}\)

\(=\frac{\sqrt{a}-1}{\sqrt{a}\left(\sqrt{a}+1\right)}\cdot\frac{\left.\left(\sqrt{a}+1\right)^2\right.}{\sqrt{a}-1}=\frac{\sqrt{a}+1}{\sqrt{a}}\)

4.2: \(Q=\frac32\)

=>\(\frac{\sqrt{a}+1}{\sqrt{a}}=\frac32\)

=>\(3\sqrt{a}=2\left(\sqrt{a}+1\right)=2\sqrt{a}+2\)

=>\(\sqrt{a}=2\)

=>a=4(nhận)