Question

x-4/x-5+x-6/x-7=x-5/x-6+x-3/x-4

Answer 1

Given x - 4/x - 5 + x - 6/x - 7 = 10/3.

LCM of x - 5, x - 7, 3  = 3(x - 5)(x-7).

 x - 4/x - 5 * 3(x - 5)(x - 7) + x - 6/x - 7 * 3(x - 5)(x - 7) = 10(x - 5)(x - 7)

3(x - 4)(x - 7) + 3(x - 6)(x - 5) = 10(x - 5)(x - 7)

6x^2 - 66x + 174 = 10x^2 - 120x + 350

6x^2 - 66x + 174 - 10x^2 + 120x - 350 = 0

-4x^2 + 54x - 176 = 0 

= -(2x^2 - 27x + 88) = 0

2x^2 - 27x + 88 = 0

2x^2 - 16x - 11x + 88 = 0

2x(x - 8) - 11(x - 88) = 0

(2x - 11)(x - 8) = 0

x = 11/2, x = 8.