Question

Solve for x :

`3/(x+1)+4/(x-1)=29/(4x-1);x!=1,-1,1/4`

 

Answer 1

`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