Question

`3/x+1-1/2=2/(3x-1),x≠-1,1/3` 

Answer 1

`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.