SOLUTION: Composite Function: Let h(t) = 5t/(t-1) and k(t) = 9/(3t+7) Find (h�k)(t) and simplify h�k(t) = h( k(t))= h[ 9/(3t+ 7)] Plug in 9/(3t+ 7) into the rule for h: 5[ 9/(3t

Question 903875: Composite Function:
Let h(t) = 5t/(t-1) and k(t) = 9/(3t+7)
Find (h�k)(t) and simplify
h�k(t) = h( k(t))= h[ 9/(3t+ 7)]
Plug in 9/(3t+ 7) into the rule for h:
5[ 9/(3t+7)] / [ 9/(3t+7) -1] =
45/( 3t+ 7)
-----------
9/(3t+ 7) -1
I understand how to solve up until this point, what do I do next?
PLEASE HELP!
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
The real trouble then is how to simplify a rational expression.

Very complicated fraction when forming the composition,

Division by a fraction is multiplying by the reciprocal,

Nothing to simplify so just perform the multiplications and simplify what is possible from that:

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