Question 1120354

3x/x-4 - 6/x^2-7x+12 = 2x/x-3
note that x^2-7x+12 is also (x-4)(x-3)
multiply both sides by x^2-7x+12
this becomes
3x(x-3)-6=2x(x-4)
3x^2-9x-6=2x^2-8x
x^2-x-6=0
(x-3)(x+2)=0
x=3 and -2
x=3 is extraneous, because two terms will have 0 in the denominator.
x=-2 is the solution

Check
-6/-6 minus 6/30=-4/-5
1-0.2=0.8 checks.