Question

I am supposed to simplify 1/a-b - 1/b-a

The answer is 2/ a-b

But I don't know how they got the denominator during the working and the final answer.
Please help, thank you

Answer 1

see explanation

Explanation:

Given

`(1)/(a-b)` -
`(1)/(b-a)`

Before subtracting the fractions, we require them to have common denominator.

Multiply the numerator/denominator of the second fraction by - 1

`(1)/(b-a)` ×
`(-1)/(-1)` =
`(-1)/(a-b)`

We now have

`(1)/(a-b)` -
`(-1)/(a-b)` ← common denominators

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

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

=
`(2)/(a-b)`