Question

evaluate the difference quotient for the given function
f(x)= 1/x, f(x)-f(a)/x-a

Answer 1

\[f(x)= 1/x\]\[f(a) = 1/2\]
\[\frac{f(x)-f(a)}{x-a} =\frac{\frac 1x -\frac 1a}{x-a} \]

Answer 2

You have to simplify it more.

Answer 3

What do I do next?

Answer 4

First simplify the numerator: \[
\frac 1 x - \frac 1 a = ?
\]

Answer 5

\[
\frac 1x - \frac 1a = \frac a{xa}-\frac x{xa} = \frac{a-x}{xa}
\]

Answer 6

So we have \[\large
\frac{\frac{a-x}{xa}}{x-a} = \frac{a-x}{(xa)(x-a)}
\]

Answer 7

and so the x-a and a-x cancels out?

Answer 8

Yeah, they cancel out to \(-1\).

Answer 9

Assuming that \(x\neq a\)

Answer 10

thank you!