a, ĐKXĐ: $a+b;a-b \neq 0$
$L=(\dfrac{a^2+b^2}{a^2-b^2})^2:[(\dfrac{a+b}{a-b}+\dfrac{a}{b})(\dfrac{a+b}{a-b}-\dfrac{b}{a})]$
$=(\dfrac{a^2+b^2}{a^2-b^2})^2):[(\dfrac{ab+b^2}{(a-b).b}+\dfrac{a^2-ab}{(a-b)b}).(\dfrac{a^2+ab}{(a-b)a}-\dfrac{ab-b^2}{(a-b)a})]$
$=(\dfrac{a^2+b^2}{a^2-b^2})^2):[(\dfrac{a^2+b^2}{(a-b)b}.\dfrac{a^2+b^2}{(a-b)a})]$
$=(\dfrac{a^2+b^2}{a^2-b^2})^2):[(\dfrac{a^2+b^2}{(a-b)^2ab)})^2]$
$=\dfrac{(a-b)^2.ab}{(a^2-b^2)^2}$
$=\dfrac{ab}{(a+b)^2}$
