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.