1/a+1 + 1/a-1

Question

I solved this out by multiplying the (a+1) by (a-1) and multiplying (a-1) with (a+1) To get (a+1)(a-1) as the denominator. Then I did the same with the numerators and got this:

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

And I got 2a/(a+1)(a-1)

But still sometimes this process confuses me so could someone please explain and solve this problem for me step by step so I actually understand it well? Thanks.

Answer 1

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

(a-1)/[(a+1)(a-1)] + (a+1)/[(a+1)(a-1)]

[ a-1+a+1 ] / [(a+1)(a-1)]

2a / (a^2-1)

so I agree with you