Precalculus Question

Question

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

Please explain with steps! thanks

Answer 1

The difference quotient is:

[1/(x+h) - 1/x]/h =

[ x - (x+h)] /x(x+h) divided by h =

-1/x(x+h)

then as h gets closer to zero, the difference quotient becomes -1/x^2