At first I assumed you meant the (t+8)^2 at the end to be the denominator for the entire term, but then I decided you must mean that only the second term is divided by (t+8)^2. Too bad, because it was easier the other way.
You have the term (t+8)^2 in the denominator of one term. You want to remove that, so factor out (t+8)^(-2) from both terms, leaving you with
(t+8)^3(6(3t-9)^5) - (3t-9)^6
--------------------------------------
(t+8)^2
Then, you can observe that you have the term (3t-9)^5 in both parts of the numerator, so you can factor that out.
(3t-9)^5 * [((t+8)^3)6 - (3t-9)]
---------------------------------------
(t+8)^2
Then we factor some 3s out of the numerator to get
That part doesn't simplify very well unfortunately.
I hope you can perform the remaining multiplication and addition, substitute, and finish the problem from there. It's best not to do someone else's homework completely for them.
Comments
*brain explodes*
(t+8)(6(3t-9)^5) - (3t-9)^6 / (t+8)^2
At first I assumed you meant the (t+8)^2 at the end to be the denominator for the entire term, but then I decided you must mean that only the second term is divided by (t+8)^2. Too bad, because it was easier the other way.
You have the term (t+8)^2 in the denominator of one term. You want to remove that, so factor out (t+8)^(-2) from both terms, leaving you with
(t+8)^3(6(3t-9)^5) - (3t-9)^6
--------------------------------------
(t+8)^2
Then, you can observe that you have the term (3t-9)^5 in both parts of the numerator, so you can factor that out.
(3t-9)^5 * [((t+8)^3)6 - (3t-9)]
---------------------------------------
(t+8)^2
Then we factor some 3s out of the numerator to get
3^5 * (t-3)^5 * 3 * [((t+8)^3)2- (t-3)]
------------------------------------------------
(t+8)^2
Let's look at the messy term [((t+8)^3)2- (t-3)].
(t+8)(t+8)(t+8)2 - t + 3
= (t^2 + 16t + 64)(t+8)2 - t + 3
= (t^3 + 16t^2 + 64t + 8t^2 + 128t + 512)2 - t + 3
= (t^3 + 24t^2 + 192t + 512)2 - t + 3
That part doesn't simplify very well unfortunately.
I hope you can perform the remaining multiplication and addition, substitute, and finish the problem from there. It's best not to do someone else's homework completely for them.
(t+8)(6(3t-9)^5)-(3t-9)^6 / (t+8)^2
(t+8)(6(3^5t^5-9^5)-(3^6*t^6-9^6)/(t^2+8^2)
(t+8)(6*3^5*6t^5-6*9^5) - (3^6*t^4-9^6)/8^2)
8(6*3^5*6t^6-6t*9^5) -8^2*3^6*t^4 -9^6*8^2
48*3^5*6t^6-48t*9^5 -8^2*3^6*t^4 -9^6*8^2
69984t^6 - 2834352t - 46656t^4 - 34012224