cho biểu thức sau: `A=((a-a^2-3)/(a^2-1)-1/(a-1)):((a+1)/(a-1)-(a-1)/(a+1)-(8\sqrt(a))/(a-1))` hãy rút gọn A?

$A=\left(\dfrac{a-a^2-3}{a^2-1}-\dfrac{1}{a-1}\right):\left(\dfrac{a+1}{a-1}-\dfrac{a-1}{a+1}-\dfrac{8\sqrt{a}}{a-1}\right)$

$=\left(\dfrac{-a^2-4}{\left(a+1\right)\left(a-1\right)}\right)\::\:\left(\dfrac{4a-8a\sqrt{a}-8\sqrt{a}}{\left(a-1\right)\left(a+1\right)}\right)$

$=\dfrac{\left(-a^2-4\right)\left(a-1\right)\left(a+1\right)}{\left(a+1\right)\left(a-1\right)\left(4a-8a\sqrt{a}-8\sqrt{a}\right)}$

$=\dfrac{\left(-a^2-4\right)\left(a+1\right)}{\left(a+1\right)\left(4a-8a\sqrt{a}-8\sqrt{a}\right)}$

$A=\dfrac{-a^2-4}{4a-8a\sqrt{a}-8\sqrt{a}}$