pre calc. help--"difference quotient"?
hey! i am having a very hard time with this pre-calculus problem..it's called "difference quotient". if anyone can, please help me, step by step. tnk you A lot!
k(t)= (t-8)^2/ t
solve for: f(t+h)-f(t)/ t
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f(t) = (t - 8)² / t ⇒
[f(t + h) - f(t)] / h
= [((t + h) - 8)² / (t + h) - (t - 8)² / t] / h
= [((t + h)² - 16(t + h) + 64) / (t + h) - (t² - 16t + 64) / t] / h
= [t((t + h)² - 16(t + h) + 64) / t(t + h) - (t² - 16t + 64)(t + h) / t(t + h)] / h
= [t((t + h)² - 16(t + h) + 64) - (t² - 16t + 64)(t + h)] / t(t + h)h
= [t((t² + 2th + h²) - 16(t + h) + 64) - (t² - 16t + 64)(t + h)] / t(t + h)h
= [t(t² + 2th + h² - 16t - 16h + 64) - (t³ - 16t² + 64t + t²h - 16th + 64h)] / t(t + h)h
= (t³ + 2t²h + th² - 16t² - 16th + 64t - t³ + 16t² - 64t - t²h + 16th - 64h) / t(t + h)h
= (t²h + th² - 64h) / t(t + h)h
= (t² + th - 64) / t(t + h)
= (t(t + h) - 64) / t(t + h)
= t(t + h) / t(t + h) - 64 / t(t + h)
= 1 - 64 / t(t + h)