Question

solve for X
(x-1/x^2-5x+6)-(x+1/x^2-4)=3/x62-x-6

Answer 1

x-1/(x-2)(x-3) - x+1/(x-2)(x+2) =3/ (x-3)(x+2)

Answer 2

From here you would combine fractions on left side
common denominator is (x-2)(x+2)(x-3)
[(x-1)(x+2) - (x+1)(x-3)]/(x-2)(x+2)(x-3) = 3/(x-3)(x+2)
Now cross multiply
3(x-2)(x+2)(x-3) = (x-3)(x+2)[(x-1)(x+2) - (x+1)(x-3)]
divide by (x+2)(x-3) on both sides, they cancel
expand and add like terms
3x - 6 = 3x + 1
which is contradiction
so there is no solution

check my math, but those are the steps