Question

Cho biểu thức: A =\(\left(\frac{a\sqrt{a}-1}{a-\sqrt{a}}-\frac{a\sqrt{a}+1}{a+\sqrt{a}}\right):\frac{a+2}{a-2}\)

a, Tìm ĐKXĐ

b, Rút gọn biểu thức A

Answer 1

a) Tìm ĐKXĐ mình làm nhắn gọn nha :v

ĐKXĐ: \(\left\{{}\begin{matrix}a>0\\a\ne1\\a\ne2\end{matrix}\right.\)

b)

\(A=\left(\frac{\sqrt{a^3}-1}{\sqrt{a}\left(\sqrt{a}-1\right)}-\frac{\sqrt{a^3}+1}{\sqrt{a}\left(\sqrt{a}+1\right)}\right):\frac{a+2}{a-2}\\ =\left(\frac{\left(\sqrt{a}-1\right)\left(a+\sqrt{a}+1\right)}{\sqrt{a}\left(\sqrt{a}-1\right)}-\frac{\left(\sqrt{a}+1\right)\left(a-\sqrt{a}+1\right)}{\sqrt{a}\left(\sqrt{a}+1\right)}\right):\frac{a+2}{a-2}\\ =\left(\frac{a+\sqrt{a}+1-a+\sqrt{a}-1}{\sqrt{a}}\right):\frac{a+2}{a-2}\\ =\frac{2\sqrt{a}}{\sqrt{a}}:\frac{a-2}{a+2}\\ =\frac{2a-4}{a+2}\)