Combine and Simplify
2 + t/t-3 - 18/t^2-9
- Please explain
We can't add fractions till they all have the same denominator. In this case, it will be (t-3)(t+3). You won't change anything if you multiply a term by 1. So, pick the value of "1" that gives you the denominator you want.
To get 2 over the denominator,
2/1 * (t-3)(t+3)/(t-3)(t+3) = 2(t-3)(t+3)/(t-3)(t+3)
t/(t-3) * (t+3)/(t+3) = t(t+3)/(t-3)(t+3)
18/(t^2-9) = 18/(t-3)(t+3)
Now we can add the fractions:
[2(t-3)(t+3) + t(t+3) - 18]/(t-3)(t+3)
=(2t^2 - 18 + t^2 + 3t - 18)/(t-3)(t+3)
= (3t^2 + 3t - 36)/(t-3)(t+3)
= 3(t^2 + t - 12)/(t-3)(t+3)
= 3(t-3)(t+4)/(t-3)(t+3)
= 3(t+4)/(t+3)