Question

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

 

 

Answer 1

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

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

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

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

=1-a