How do you use the difference quotient with fractions?


Finding the difference quotient when your function is a fraction can be confusing, but there's actually a really easy way to handle it!

You'll need to find the difference quotient the same way you would for any other kind of non-fraction function, to start. The thing that makes these problems tricky is that, when you do that, you'll end up with "little fractions" inside of a "big fraction".

The trick to getting rid of those little fractions is to multiply both the numerator and denominator of the big fraction by the common denominator of the little fractions. That way, you'll get the fractions to cancel out in one simple, quick step.

Then you'll just be able to multiply out and simplify the numerator, and then hopefully cancel out an "h" from the numerator and denominator. This is a process that will work every time when you're trying to find the difference quotient for a fraction.

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