Question 1015205
What you need to do is find A and B such that
{{{(x-1)/(x^2-4) = A/(x+2) + B/(x-2)}}}
After multiplying by the common denominator
x-1 = A(x-2) + B(x+2)
x-1 = Ax - 2A + Bx + 2B
this means
A + B = 1  and
2B - 2A = -1
B - A = -1/2
Now add these and get
2B = 1/2
B = 1/4
A = 3/4