Difference Quotient...4

[nycmathguy]

Chapter 1
Calculus 1

Question 29

I know that f(a) = 1/a.

On the numerator we have:

(1/x) - (1/a)

LCD = ax

Our numerator now becomes:

(a - x)/ax

The original problem becomes

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

Multiply (a - x) by -1 to get x - a.

We now have (x - a)/(ax) ÷ (x - a).


(x - a)/(ax) • 1/(x - a)

Answer: 1/(ax).

What does the answer mean?

 

[MathLover1]

Answer should be: -1/(ax)

reason:

since numerator is (a-x)/xa, we factor out 1- to make -(x-a)/xa so we can cancel denominator

-> your answer

 

[nycmathguy]

Answer should be: -1/(ax)

reason:
View attachment 2349

View attachment 2350

since numerator is (a-x)/xa, we factor out 1- to make -(x-a)/xa so we can cancel denominator

View attachment 2351

View attachment 2352-> your answer

Look: 1/ax = 1/xa. The only problem is the fact that I forgot to include the negative sign.