Question

[Duong Thi Nhuong]

Rút gọn: \(\left(\frac{a\sqrt{a}-3}{a-2\sqrt{a}-3}-\frac{2\left(\sqrt{a}-3\right)}{\sqrt{a}+1}+\frac{\sqrt{a}+3}{3-\sqrt{a}}\right)\div\frac{a+8}{a-1}\)

Answer 1

[Nguyễn Lê Phước Thịnh]

\(=\dfrac{a\sqrt{a}-3-2\left(a-6\sqrt{a}+9\right)-a-4\sqrt{a}-3}{\left(\sqrt{a}-3\right)\left(\sqrt{a}+1\right)}\cdot\dfrac{a-1}{a+8}\)

\(=\dfrac{a\sqrt{a}-a-4\sqrt{a}-6-2a+12\sqrt{a}-18}{\left(\sqrt{a}-3\right)}\cdot\dfrac{\sqrt{a}-1}{a+8}\)

\(=\dfrac{a\sqrt{a}-3a+8\sqrt{a}-24}{\left(\sqrt{a}-3\right)}\cdot\dfrac{\sqrt{a}-1}{a+8}=\sqrt{a}-1\)