Question

x-1/x-2 + x-3/x-4=10/3

Answer 1

( (x-1)(x-4)+(x-3)(x-2) )/(x-2)(x-4) = 10/3
( x2 -5x +4 + x2 - 5x +6 )/( x2 - 6x + 8) = 10/3
(x2 -5x +5)/x2 -6x +8 = 5/3
3x2 -15x + 15 = 5x2 -30x + 40
2x2 -15x +25 = 0
2x2 - 10x -5x +25 =0
2x(x- 5) - 5 (x -5) =0
(2x-5)(x-5) =0
x = 5/2 or x = 5