Question

Solve `(2x)/(x - 3) + 1/(2x + 3) + (3x + 9)/((x - 3)(2x +3)) = 0; x != 3, x != - 3/2`

Answer 1

`(2x)/(x - 3) + 1/(2x + 3) + (3x + 9)/((x - 3)(2x +3)) = 0; x != 3, x != - 3/2`

`=> (2x(2x + 3) + 1(x - 3) + 3x + 9)/((x - 3)(2x + 3)) = 0`

`=> 4x^2 + 6x + x - 3 + 3x + 9 = 0`

`=> 4x^2 + 10x  + 6 = 0`

`=> 4x(x + 1) + 6(x + 1) = 0`

`= (x + 1)(4x + 6) = 0`

`=> x + 1 = 0 or 4x + 6 = 0`

`=> x = -1 or x = (-6)/4 = (-3)/2` (reject)