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Question
Solve for x :
`3/(x+1)+4/(x-1)=29/(4x-1);x!=1,-1,1/4`
Solution
`3/(x+1)+4/(x-1)=29/(4x-1)`
`=>(3(x-1)+4(x+1))/((x+1)(x-1))=29/(4x-1)`
`=>(3x-3+4x+4)/((x+1)(x-1))=29/(4x-1)`
`=>(7x+1)/(x^2-1)=29/(4x-1)`
⇒(7x+1)(4x−1)=29(x2−1)
⇒28x2+4x−7x−1=29x2−29
⇒28x2−3x−1=29x2−29
⇒x2+3x−28=0
⇒x2+7x−4x−28=0
⇒x(x+7)−4(x+7)=0
⇒(x+7)(x−4)=0
⇒x+7=0 or x−4=0
⇒x=−7 or x=4
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