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Question
`3/x+1-1/2=2/(3x-1),x≠-1,1/3`
Solution
`3/x+1-1/2=2/(3x-1),x≠-1,1/3`
⇒`3/x+1-2/(3x-1),x≠-1, 1/3`
⇒` (9x-3-2x-2)/((x+1) (3x-1))=1/2`
⇒`( 7x-5)/(3x^2+2x-1)=1/2`
⇒` 3x^2+2x-1=14x-10` (Cross multiplication)
⇒ `3x^2-12x+9=0`
⇒ `x^2-4x+3=0`
⇒` x^2-3x-x+3=0`
⇒` x(x-3) -1 (x-3)=0`
⇒` (x-3) (x-1)=0`
⇒` x-3=0 or x-1=0`
⇒x=3 or x=1
Hence, 1 and 3 are the roots of the given equation.
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