Question

$frac{a}{a^2-3a} + frac{a-8}{a} + frac{7a^2-3a-72}{a^3-9a}$

Answer 1

a/a(a-3) + (a-8)/a +(7a² -3a-72)/a(a+3)(a-3) =
 ( a(a+3) + (a+8)(a² -9) +7a² -3a-72 )/a(a-3)(a+3) =
(a² +3a +a³ +8a² -9a -72 +7a² -3a-72)/a(a-3)(a+3) =
(a³ +16a² -9a -144)/a(a-3)(a+3 )= ( a²(a+16) -9(a+16) ) / a(a-3)(a+3) =
 (a² -9)(a+16) / a(a² -9) =(a+16)/a.