[tex] \frac{a}{a^2-3a} + \frac{a-8}{a} + \frac{7a^2-3a-72}{a^3-9a} [/tex]

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.