Perform the indicated operation. Simplify if u can?

Question

u+12/u^2 + u+2/3u???

Answer 1

u+12/u^2 + u+2/3u

u^3 + 12 + u^3 +2u/3
2u^3 + 2u/3 + 12
6u^3 +2u + 36

Answer 2

(u+12)/u^2 +(u+2)/(3u) Is this what you meant? If so
3(u+12)/(3u^2) + u(u+2)/(3u^2)
= (3u + 36 +u^2 +2u)/(3u^2)
=(u^2 +5u +36)/(3u^2)

Answer 3

since v^2 - 81 = (v + 9)(v - 9) (v-7)/(v-9) - (v+1)/(v+9) + (v-45)/(v^2-81) = [(v - 7)(v + 9) - (v + 1)(v - 9) + (v - 45)]/(v^2 - 81) = [(v^2 + 2v - 63) - (v^2 - 8v - 9) + (v - 45)]/(v^2 - 81) = (10v - 54 + v - 45)/(v^2 - 81) = (11v - 99)/(v^2 - 81) = [11(v - 9)]/(v^2 - 81) = [11(v - 9)]/[(v + 9)(v - 9)] = 11/(v + 9)