Question

Solve the following quadratic equations by factorization:

`(x-1)/(x-2)+(x-3)/(x-4)=3 1/3`, x ≠ 2, 4

Answer 1

We have been given

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

3(x² - 5x + 4 + 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,

2x - 5 = 0

2x = 5

x = 5/2

or,

x - 5 = 0

x = 5

Hence, x = 5/2 or x = 5