Answer:
[tex] x = \dfrac{6 - a}{a + 3} [/tex]
Step-by-step explanation:
[tex] \dfrac{3x - 2}{a^2 - 2a} + \dfrac{x - 1}{a - 2} + \dfrac{2}{a} = 0 [/tex]
Factor all denominators.
[tex] \dfrac{3x - 2}{a(a - 2)} + \dfrac{x - 1}{a - 2} + \dfrac{2}{a} = 0 [/tex]
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.
[tex] a(a - 2)[\dfrac{3x - 2}{a(a - 2)} + \dfrac{x - 1}{a - 2} + \dfrac{2}{a}] = 0 \times a(a - 2)[/tex]
[tex] a(a - 2) \times \dfrac{3x - 2}{a(a - 2)} + a(a - 2) \times \dfrac{x - 1}{a - 2} + a(a - 2) \times \dfrac{2}{a}] = 0 [/tex]
[tex] 3x - 2 + a(x - 1) + 2(a - 2) = 0 [/tex]
[tex] 3x - 2 + ax - a + 2a - 4 = 0 [/tex]
[tex] 3x + ax + a - 6 = 0 [/tex]
[tex] x(a + 3) = 6 - a [/tex]
[tex] x = \dfrac{6 - a}{a + 3} [/tex]
