solve the ration equation: 2x/x-4 - 2x-5/x^2-10x+24= -3/x-6

Answer 1

Maybe could you mean:
2x / (x-4) - (2x-5) / (x^2-10x+24) = -3/ (x-6 )

now luckily 24 = 4 * 6 so we know what to do
2x / (x-4) - (2x-5) / [ (x-4)(x-6) ] = -3/ (x-6 )
first term by (x -6) / (x-6) etc so they are all (x-4)(x-6) on the bottom
2x(x-6) - (2x-5) = -3 (x-4)
2 x^2 - 12 x - 2 x + 5 = -3 x + 12
2 x^2 - 11 x - 7 = 0
I get 6.07 and -0.576