+128407 3x + 4
___________ we can solve this with partial fractions
x^2 -6x + 5
3x + 4 A B
___________ = _____ + ____ multiply through by (x -5) ( x - 1)
(x - 5) ( x - 1) x - 1 x - 5
3x + 4 = A(x - 5) + B ( x - 1)
3x + 4 = Ax - 5A + Bx - B
3x + 4 = (A + B) x - (5A + 5B) equate coefficients
A + B = 3
-5A - B = 4 add these equations
-4A = 7
A = -7/4
And
(-7/4) + B = 3
-7/4 + B = 12/4
B = 19/4
So the solution is
3x+4 - 7 19
__________ = _________ + ________
x^2 - 6x + 5 4 ( x - 1) 4 (x - 5)
