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Question
`4/x-3=5/(2x+3),x≠0,-3/2`
Solution
`4/x-3=5/(2x+3),x≠0,-3/2`
⇒` 4/x-5/(2x+3)=3`
⇒`(8x+12-5x)/(x(2x+3))=3`
⇒`(3x+12)/(2x^2+3x)=3`
⇒`(x+4)/(2x^2+3x)=3`
⇒`2x^2+3x=x+4` (Cross multiplication)
⇒`2x^2+2x-4=0`
⇒`x^2+x-2=0`
⇒`x^2+2x-x-2=0`
⇒`x(x+2)-1(x+2)=0`
⇒`(x+2)(x-1)=0`
⇒` x+2=0 or x-1=0`
⇒ `x=-2 or x=1`
Hence, -2 and 1 are the roots of the given equation.
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