Answer:
(t-3)/(t+2)
Step-by-step explanation:
1 - 2/(t+3)
-------------------
2/(t^2-9) +t/(t-3)
Factor the denominator
1 - 2/(t+3)
-------------------
2/(t-3)(t+3) +t/(t-3)
Multiply the top and bottom bottom by (t-3)(t+3)/ (t-3)(t+3) to clear the fraction
( 1 - 2/(t+3)) * (t-3)(t+3)
-------------------
2/(t-3)(t+3) +t/(t-3) * (t-3)(t+3)
(t-3)(t+3) - 2(t-3)
-------------------
2 +t(t+3)
Distribute
t^2-3t+3t-9 - 2t+6
-------------------
2 +t^2+3t
Combine like terms
t^2-2t-3
-------------------
t^2+3t+2
Factor
(t-3) (t+1)
-------------------
(t+2) (t+1)
Cancel like terms
(t-3)
-------------------
(t+2)
