Question

1/(a-b) + 4/(b-a) - 8/(a+b) - (11a - 5b)/(b^2-a^2) does this equal (22a-10b)/(b^2-a^2)?

Answer 1

I told you it was 0.

Check all your signs.

Answer 2

First, we make (a-b) = -(b-a):
[1/(a-b) - 4/(a-b)] - 8/(a+b) - (11a - 5b)/(b^2-a^2)
Subtracting the first two fractions:
-3/(a-b) - 8/(a+b)) - (11a - 5b)/(b^2-a^2)
Gathering the first two fractions into one fraction:
(-3a - 3b - 8a + 8b)/(a-b)(a+b) - (11a - 5b)/(b^2-a^2)
Equals:
(-11a + 5b)/(a^2 - b^2)
Doing the same as the first step:
(11a - 5b)/(b^2 - a^2)

Answer 3

Of course, note that: (b-a)(b+a) = (b^2 - a^2), right?