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Question
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 + 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.
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