Evaluate the difference quotient for the given function Simp

Evaluate the difference quotient for the given function. Simplify your answer. f(x) = 1/x, f(x) - f(a)/x - a

Solution

f(x)=1/x

f(a)=1/a

[f(x) -f(a)]/[x-a]

=[(1/x) -(1/a)]/[x-a]

=[(a-x)/(xa)]/[x-a]

=[-(x-a)/(xa)]/[x-a]

=-1/(xa)

difference coefficient =-1/(xa)