Giải thích các bước giải:
Ta có:
$A=\dfrac{u+10}{u-2}+\dfrac{u-18}{u-2}+\dfrac{u+2}{u^2-4}$
$\to A=\dfrac{(u+2)(u+10)}{(u+2)(u-2)}+\dfrac{(u-18)(u+2)}{(u+2)(u-2)}+\dfrac{u+2}{(u+2)(u-2)}$
$\to A=\dfrac{(u+2)(u+10)+(u-18)(u+2)+u+2}{(u+2)(u-2)}$
$\to A=\dfrac{u^2+12u+20+u^2-16u-36+u+2}{(u+2)(u-2)}$
$\to A=\dfrac{2u^2-3u-14}{(u+2)(u-2)}$
$\to A=\dfrac{(2u^2+4u)-(7u+14)}{(u+2)(u-2)}$
$\to A=\dfrac{2u(u+2)-7(u+2)}{(u+2)(u-2)}$
$\to A=\dfrac{(2u-7)(u+2)}{(u+2)(u-2)}$
$\to A=\dfrac{2u-7}{u-2}$