Question

How do I solve this?​

Answer 1

`x = (6 - a)/(a + 3)`

Explanation:

`(3x - 2)/(a^2 - 2a) + (x - 1)/(a - 2) + (2)/(a) = 0`

Factor all denominators.

`(3x - 2)/(a(a - 2)) + (x - 1)/(a - 2) + (2)/(a) = 0`

There are 3 denominators: a(a - 2), a - 2, and a.

The LCD is a(a - 2).

Multiply both sides of the equation by the LCD.

`a(a - 2)[(3x - 2)/(a(a - 2)) + (x - 1)/(a - 2) + (2)/(a)] = 0 * a(a - 2)`

`a(a - 2) * (3x - 2)/(a(a - 2)) + a(a - 2) * (x - 1)/(a - 2) + a(a - 2) * (2)/(a)] = 0`

`3x - 2 + a(x - 1) + 2(a - 2) = 0`

`3x - 2 + ax - a + 2a - 4 = 0`

`3x + ax + a - 6 = 0`

`x(a + 3) = 6 - a`

`x = (6 - a)/(a + 3)`