Question

compute difference quotient of -1/(x-5)

Answer 1

im supposed to use f(a+h)-f(a)/h

Answer 2

any ideas? you have to compute
\[\frac{\frac{-1}{a+h-5}+\frac{1}{a-5}}{h}\]

Answer 3

lets forget the h for a moment and concentrate on the numerator, because that is where all the algebra is

Answer 4

\[\frac{1}{a-5}-\frac{1}{a+h-5}\]
\[\frac{a+h-5-(a-5)}{(a-5)(a+h-5)}\]
\[\frac{h}{(a-5)(a+h-5)}\]

Answer 5

now divide by h, and of course the h cancels, leaving
\[\frac{1}{(a-5)(a+h-5)}\]