Question

Bài : Ch.minh đẳng thức 
\(\left(1-\dfrac{a-\sqrt{a}}{\sqrt{a}-1}\right)\)+ \(\left(1+\dfrac{a+\sqrt{a}}{1+\sqrt{a}}\right)\) = 1-a với a ≥ 0 và a ≠ 1

Answer 1

\(\left(1-\dfrac{a-\sqrt{a}}{\sqrt{a}-1}\right)+\left(1+\dfrac{a+\sqrt{a}}{1+\sqrt{a}}\right)\left(dkxd:a\ge0;a\ne1\right)\)

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

\(=1-\sqrt{a}+1+\sqrt{a}\)

\(=2\)

Bạn xem lại đề bài nhé!

Answer 2

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

Sửa lại đề nhé !