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Question
`x/(x+1)+(x+1)/x=2 4/15, x≠ 0,1`
Solution
`x/(x+1)+(x+1)/x=2 4/15, x≠ 0,-1`
⇒ `x^2+(x+1)^2/(x(x+1))=34/15`
⇒ `(x^2+x^2+2x+1)/(x^2+x)=34/15`
⇒`( 2x^2+2x+1)/(x^2+x)=34/15`
⇒`30x^2+30x+15=34x^2+34x`
⇒`4x^2+4x-15=0`
⇒`4x^2+10x-6x-15x=0`
⇒`2x(2x+5)-3.(2x+5)=0`
⇒ `(2x+5) (2x-3)=0`
⇒`2x+5=0 or 2x-3=0`
⇒` x=-5/2 or 2x-3=0`
Hence,`5/2` and` 3/2` are the roots of the given equation.
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