Question

Suppose that f(x) = 1/x. Find a simplified expression for f(x)-f(a)/x-a

Answer 1

f(x) = 1/x
so, f(a) = 1/a

(f(x) - f(a))/(x-a) , notice the necessary placing of brackets
= (1/x - 1/a)/(x-a)
= [ (a-x)/(ax) ]/(x-a)
= (a-x)/(ax) * 1/(x-a)
= -1/(ax)

notice (a-x)/(x-a)
= -(x-a)/(x-a) = -1

Answer 2

got it, thanks!