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

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


   

Question 903875: Composite Function:
Let h(t) = 5t/(t-1) and k(t) = 9/(3t+7)
Find (hºk)(t) and simplify
hºk(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) About Me  (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, %28%285%289%2F%283t%2B7%29%29%29%2F%28%289%2F%283t%2B7%29%29-1%29%29

%285%283t%2B7%29%2F9%29%2F%28%289%2F%283t%2B7%29%29-%283t%2B7%29%2F%283t%2B7%29%29%29

%285%283t%2B7%29%2F9%29%2F%28%282-3t%29%2F%283t%2B7%29%29

Division by a fraction is multiplying by the reciprocal,
%28%285%283t%2B7%29%29%2F%289%29%29+%2A+%28%283t%2B7%29%2F%282-3t%29%29

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

%285%289t%5E2%2B42t%2B49%29%29%2F%2818-27t%29

highlight%28%2845t%5E2%2B210t%2B245%29%2F%2818-27t%29%29