Question 1140273
Multiply everything by (x-5)(x+2)
the left side is 5x+31
the right side is a(x+2)-b(x-5)
so ax+2a-bx+5b=5x+31
x(a-b)+2a+5b=5x+31; set the x term=5 and the constant term=31
a-b=5
2a+5b=31
5a-5b=25
so 7a=56, a=8
b=3
(8, 3)

check with x=7
66/(18)=(8/2)-3/9=3 2/3 checks