# Solve for x : (2x)/(x-3)+1/(2x+3)+(3x+9)/((x-3)(2x+3)) = 0, x!=3 - Mathematics

Solve for x

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

#### Solution

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+x3+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.

Concept: Solutions of Quadratic Equations by Factorization
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