Find f'(a). f(t)=(5t+5)/(t+6)
Here is what I have so far
f(t)=(5t+5)/(t+6)
=f'(a)=lim t-a (5t+5)/(t+6)-(5a+5)/(a+6)/t-a
=(5t+5)(a+6)-(5a+5)(t+6)/(t+6)(a+6)
=5ta+5a+30t+30-5at-5t-30a-30/(t+6)(a+6)
=25t-25a/(t+6)(a+6)
=25t-25a/(t+6)(a+6)(t-a)
=25/(t+6)(a+6)
This limit can now be evaluated to conclude that f'(a)=lim t-a 25/(t+6)(a+6)
Here is where I am stuck and not sure where to go. I have tried the FOIL technique with the denominator. I need some help trying to figure out the limit.
