Pre-calculus question?

Question

Find the difference quotient.

f(t)=1/t
f(t)-f(1)/t-1 where t does not equal 0

I need to learn this, and explanation would be greatly appreciated =)

Answer 1

So just plug it in and simplify. The difference quotient is
((1/t)-1)/(t-1) which simplifies to
((1-t)/t)/(t-1) where stuff cancels and you get
-1/t.

Answer 2

[f(t)-f(1)]/(t-1)
= (1/t - 1)/(t-1)
= [(1-t)/t]/(t-1)
= -1/t

Answer 3

f(t) = 1 / t
f(1) = 1
f(t) - f(1) = 1 / t - 1 = (1 - t) / t

f(t) - f(1) / (t - 1)
= (1 - t) / [ (t) (t - 1) ]
= - (t - 1) / [ (t) (t - 1) ]
= - 1 / t