Question

Solve : 4/x-3 + 2/x-2 = 6/x

Answer 1

x =
`(9)/(4)` or 2.5

Explanation:

`(4)/(x-3) + (2)/(x-2) = (6)/(x)`

Finding L.C.M. of (x - 3) and (x - 2)

`(4(x-2) + 2(x-3) )/((x-3)(x-2)) = (6)/(x)`

`((4x-8) + (2x-6))/(x^(2) - 3x-2x+6)=(6)/(x)`

`(4x-8 +2x-6)/(x^(2) -5x +6) = (6)/(x)`

`(6x-14)/(x^(2) -5x+6)= (6)/(x)`

Cross multiplying:

x (6x - 14) = 6 (x² - 5x +6)

6x² - 14x = 6x² - 30x + 36

Cancelling 6x² from both the sides:

- 14x = - 30x + 36

30x - 14x = 36

16x = 36

x =
`(36)/(16)`

∴ x =
`(9)/(4)` or 2.5