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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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)
Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”
So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student—from basic middle school classes to advanced college calculus—figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: http://www.kristakingmath.com
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Tagged under: calculus,fractions,big fraction,common denominator,difference quotient fractions,difference quotient,Krista King,educational, fractions
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