Question

How do you combine `( x-1 ) / ( x^2-1 ) + (2 )/ (5x+5)`?

Answer 1

Start by factoring the two denominators

`(x^2-1) = x^2 - 1^2 = (x-1)(x+1)`

and

`5x + 5 = 5(x+1)`

Your expression will become

`E = cancel(x-1)/(cancel((x-1)) * (x+1)) + 2/(5(x+1))`

Multiply the nominator and the denominator of the first fraction by 5 to get the two fractions to have a common denominator. This will allow you to add the nominators and get the final form of the expression

`(5 * 1)/(5 * (x+1)) + 2/(5(x+1)) = (5 + 2)/(5(x+1)) = 7/(5(x+1))`