MHB Simplifying the Difference Quotient for f(x) = 1/x

[tmt1]

I have a problem:

f(x) = 1/x,

[f(x) - f(a)] / x- a

I am wondering how to approach this problem.

I have so far.

(1/x - 1/a) / (x-a)

([a-x] / xa) / (x-a)

How would I simplify this?

By the way, the answer is

-1 / ax

 

[mathbalarka]

Here's a re-write of your own approach using $\LaTeX$

$$\frac{f(x) - f(a)}{x - a} = \frac{\frac1{x} - \frac1{a}}{x - a} = \frac{\frac{a-x}{ax}}{x - a} = \frac{a - x}{ax(x-a)}$$

Can you use the fact $a - x = -(x-a)$?