Question

rút gọn

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

Answer 1

\(A=\left(\dfrac{\sqrt{a}}{2}-\dfrac{1}{2\sqrt{a}}\right)\left(\dfrac{\sqrt{a}-1}{\sqrt{a}+1}-\dfrac{\sqrt{a}+1}{\sqrt{a}-1}\right)=\left(\dfrac{a}{2\sqrt{a}}-\dfrac{1}{2\sqrt{a}}\right)\left[\dfrac{\left(\sqrt{a}-1\right)^2}{\left(\sqrt{a}+1\right)\left(\sqrt{a}-1\right)}-\dfrac{\left(\sqrt{a}+1\right)^2}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}\right]=\dfrac{a-1}{2\sqrt{a}}.\left(\dfrac{a-2\sqrt{a}+1}{a-1}-\dfrac{a+2\sqrt{a}+1}{a-1}\right)=\dfrac{a-1}{2\sqrt{a}}.\dfrac{a-2\sqrt{a}+1-a-2\sqrt{a}-1}{a-1}=\dfrac{\left(a-1\right)\left(-4\sqrt{a}\right)}{2\sqrt{a}\left(a-1\right)}=-2\)