Question

Thu gọn biểu thức:

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

Answer 1

ĐKXĐ: \(a>0;a\ne1\)

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

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

\(=\dfrac{a+\sqrt{a}-2-a+\sqrt{a}+2}{\sqrt{a}}=2\)