Question

`16/x-1=15/(x+1),x≠0,-1`

Answer 1

`16/x-1=15/(x+1),x≠0,-1`  

⇒ `16/x-15/(x+1)=1` 

⇒ `(16x+16-15x)/(x(x+1))=1` 

⇒ `(x+16)/(x^2+x)=1` 

⇒`x^2+x=x+16`                (Cross multiplication)

⇒`x^2-16=0` 

⇒`(x+4) (x-4)=0`  

⇒`x+4=0  or  x-4=0` 

⇒`x=-4  or  x=4` 

Hence, -4 and 4 are the roots of the given equation.