Question

Find for x :-
(x-1)/(x+1) + (x-3)/(x-4) = 10/3

Answer 1

(x-1)/(x-2) + (x-3)/(x-4) = 10/3 …(1)

3(x-1)(x-4) + 3(x-3)(x-2) = 10(x-2)(x-4), or

3(x^2–5x+4) + 3(x^2–5x+6) = 10(x^2–6x+8) or

3x^2 - 15x + 12 + 3x^2 - 15x + 18 = 10x^2 - 60 x +80, or

10x^2 - 60 x +80 - [3x^2 - 15x + 12 + 3x^2 - 15x + 18] = 0, or

10x^2 - 60 x +80 -3x^2 + 15x - 12 - 3x^2 + 15x - 18 = 0, or

4x^2 -30x +50 = 0, or

2x^2 - 15x + 25 = 0, or

2x^2–5x - 10x + 25 = 0, or

x(2x-5) - 5(2x-5) = 0, or

(x-5)(2x-5) = 0, or

x = 5 or 5/2.