Question

Solve for x

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

Answer 1

Given:

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

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

⇒ 4x² + 6x + x − 3 + 3x + 9 = 0

⇒ 4x² + 10x + 6 = 0

⇒ 4x² + 4x + 6x + 6 = 0

⇒ 4x(x + 1) + 6(x + 1) = 0

⇒(x + 1) (4x + 6) = 0

⇒x + 1 = 0 or 4x + 6 = 0

`=>x=-1,-3/2`

But 

`x !=-3/2`

Thus, x = −1 is the solution of the given equation.