Question

Solve the following quadratic equations by factorization:

`1/(x-2)+2/(x-1)=6/x` , x ≠ 0

Answer 1

We have been given

`1/(x-2)+2/(x-1)=6/x`

x² - x + 2x² - 4x = 6(x² - x - 2x + 2)

3x² - 13x + 12 = 0

3x² - 9x - 4x + 12 = 0

3x(x - 3) - 4(x - 3) = 0

(3x - 4)(x - 3) = 0

Therefore,

3x - 4 = 0

3x = 4

x = 4/3

Or,

x - 3 = 0

x = 3

Hence, x = 4/3 or x = 3