If g(x) = 1/x and h is a nonzero real number, then (g(x+h) - g(x))/h =

Question

 If g(x) = 1/x and h is a nonzero real number, then (g(x+h) - g(x))/h = 

Answer 1

 

If       g(x) = 1/x 

then   g(x+h) = 1/(x+h)  ,(replacing x by x+h on both side)

 

So,

   

(g(x+h) - g(x))/h = (  1/(x+h)  -  1/x ) / h

                          = (  x/x(x+h)  -  (x+h)/x(x+h) )/ h    ( take LCM )

                          = (  ( x-x-h)/x(x+h) ) / h

                          =( -h/ x(x+h) )/ h

                          =  -h/ (xh(x+h))

                          = -1 /x(x+h)