Question

Solve the following quadratic equations by factorization:
Solve for x:
(x-1/x-2)+(x-3/x-4)=3(1/3),x≠2,4

Answer 1

x = +5, +5/2

Step-by-step explanation:

x≠2,4

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

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

3(x² - 5x + 4) + 3(x² - 5x + 6) = 10(x² - 6x + 8)

-4x² +30x -50 = 0

 2x² - 15x +25 = 0

 2x² - 10x -5x +25 = 0

 2x (x - 5) -5 (x - 5) = 0

 (2x -5)(x-5) = 0

 Therefore x = +5, +5/2