Question

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

Answer 1

Multiply the equ with (x-3)(2x+3) both the sides we get 2x (2x+3) + (x-3) + (3x+9) =0 => 4x^2 +6x +x -3 +3x +9 =0 => 4x^2 +10x +6 =0 => 2x^2 +5x +3 =0 => 2x^2 +2x +3x +3 =0 => 2x (x+1) +3(x+1) =0 => (x+1)(2x+1)=0 => x= -1 and x= -1/2 answer

Answer 2

$2x (2x+3) + (x-3) + (3x+9) =0$
$4x^2 +6x +x -3 +3x +9 =0$
$4x^2 +10x +6 =0$
$2x^2 +5x +3 =0$
$2x^2 +2x +3x +3 =0$
$2x (x+1) +3(x+1) =0$
$(x+1)(2x+1)=0$
$x=-1$  or  $x=-1/2$