how to find the difference quotient and simplify the answer

[Ray 4]

1. The problem statement, all variables and given/known data

find the difference quotient and simply your answer.

f(t)=1/t, [f(t)-f(1)]/t-1, t doesn't equal 1


2. Relevant equations
the book says the answer is -1/t, t doesn't equal 1


3. The attempt at a solution

(1/t-1)/t-1

(1/t-t/t)/t-1

(-1t/t)/t-1

-1/t-1


thanks!!!

[danago]

1. The problem statement, all variables and given/known data

find the difference quotient and simply your answer.

f(t)=1/t, [f(t)-f(1)]/t-1, t doesn't equal 1


2. Relevant equations
the book says the answer is -1/t, t doesn't equal 1


3. The attempt at a solution

(1/t-1)/t-1

(1/t-t/t)/t-1

(-1t/t)/t-1

-1/t-1


thanks!!!

How did you get that line?

[Ray 4]

How did you get that line?

i thought that's what you get when you minus t/t from 1/t

[chislam]

Nope, you get:

\frac{1-t}{t}

instead of:

\frac{-t}{t}