Question

`1/x-1-1/(x+5)=6/7,x≠1,-5` 

Answer 1

`1/x-1-1/(x+5)=6/7,x≠1,-5`  

⇒` (x+5-x+1)/((x-1) (x+5))=6/7` 

⇒`6/(x^2+4x-5)=6/7` 

⇒`x^2+4x-5=7` 

⇒`x^2+4x-12=0` 

⇒`x^2+6x-2x-12=0` 

⇒`x(x+6)-2(x+6)=0` 

⇒`(x+6)(x-2)=0` 

⇒`x+6=0  or  x-2=0` 

⇒` x=-6  or  x=2` 

Hence, -6 and 2 are the roots of the given equation.