1/a+1 + 1/a-1

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.

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

To solve the expression 1/(a+1) + 1/(a-1), we need to find a common denominator and combine the fractions.

Step 1: Identify the denominators
The denominators are (a+1) and (a-1).

Step 2: Finding the common denominator
To find the common denominator, we multiply the two denominators together:
Common Denominator = (a+1)(a-1)

Step 3: Rewrite the fractions with the common denominator
We rewrite 1/(a+1) and 1/(a-1) with the common denominator:
1/(a+1) = (a-1)/[(a+1)(a-1)]
1/(a-1) = (a+1)/[(a+1)(a-1)]

Step 4: Add the fractions
Now that we have the fractions with the same denominator, we can add them together:
[(a-1) + (a+1)]/[(a+1)(a-1)]

Step 5: Simplify the numerator
Combine like terms in the numerator:
(2a)/[(a+1)(a-1)]

So, the final simplified expression is 2a/[(a+1)(a-1)].