1. ## Simplification

Hi all

This is probably a piece of cake for most of you, but I haven't dealt with math in years so I could use a little help.

(1/a + 1/b) (1/a - 1/b)

So this is the starting point and it needs to be simplified. I have this from a friend and he said the solution is (1+a)/b . I'm not sure if that's correct, that's what I'm trying to find out.

This is how far I got:

(b^2 - a^2) / (a^2 * b^2)

And then (1 - a^2 / b^2) / a^2

From there I just go in circles... I'd appreciate if someone could tell me how to get to that solution (if it's correct...).

Thanks

2. ## Re: Simplification

The expression is also equal to $\frac{1}{a^2} - \frac{1}{b^2}$ by difference of two squares (so your answer is correct).

I don't think your friend's answer is correct. For example, you could let a = b = 2, in which the correct answer is 0, but (1+a)/b = 3/2.