Evaluate the difference quotient for f(x) = 1/2 Simplify your answer.

f(x) - f(a) / x -a
f(1/2) - (a/1) / x-a
what allows me to times xa to the numerator to the denominator. for example:

(1/x) - (1/a) *ax / (x-a) *ax is this a rational expression rule? or another rule?

(x-a)/ (x-a)(ax) = This is another part that has confused me for the solution because the next part says -(x-a) / (a-x)(ax)

Question

Evaluate the difference quotient for f(x) = 1/2 Simplify your answer.

 f(x) - f(a) / x -a
f(1/2) - (a/1) / x-a
what allows me to times xa to the numerator to the denominator.  for example:

(1/x) - (1/a) *ax / (x-a) *ax is this a rational expression rule? or another rule?

(x-a)/ (x-a)(ax) = This is another part that has confused me for the solution because the next part says -(x-a) / (a-x)(ax)<---where does the negative in front of -(x-a) come from in the numerator?   answer = -1/ax