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Question
`x/(x-1)+x-1/4=4 1/4, x≠ 0,1`
Solution
`x/(x-1)+x-1/4=4 1/4, x≠ 0,1`
⇒`x^2+(x-1)^2/(x(x-1))=17/4`
⇒` (x^2+x^2-2x+1)/(x^3-x)=17/4`
⇒ `(2x^2-2x+1)/(x^2-1)=17/4`
⇒ `8x^2-8x+4=17x^2-17x`
⇒`9x^2-9x-4=0`
⇒`9x^2-12x+3x-4=0`
⇒ `3x(3x-4)+1(3x-4)=0`
⇒ `(3x-4) (3x+1)=0`
⇒`3x-4=0 or 3x+1=0`
⇒` x=4/3 or x=-1/3`
Hence,`4/3` and `1/3` are the roots of the given equation.
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