Question

Rút gọn biểu thức B = ((1 - a * sqrt(a))/(1 - sqrt(a)) + sqrt(a)) * ((1 - sqrt(a))/(1 - a)) ^ 2

Answer 1

ĐKXĐ: \(\left\{{}\begin{matrix}a>=0\\a< >1\end{matrix}\right.\)

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

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

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

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

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