Question

3/x^2-3x+4/x=1/x-3, please HELP

Answer 1

multiply both sides by the LCM which is x^2(x-3)

3(x-3) - (3x+4)(x(x-3)) = x^2

3x - 9 - (3x+4)(x^2-3x) = x^2
3x - 9 - 3x^3 -9x^2 + 4x^2 -12x = x^2
-3x^3 -x^2 -5x^2 + 3x - 12x = 9
-3x^3 - 6x^2 - 9x = 9
-3x(x^2 - 2x - 3) = 9
x(x^2 - 2x -3) = -3

x = -3; (x-3)(x+1)=-3
so x = -3; x = 0; x= -4