00:03
We're going to evaluate this difference quotient for the function f of x equals 1 over x.
00:09
Notice that we need to know f of a.
00:11
So f of a is going to be 1 over a.
00:15
Okay.
00:17
So now let's substitute f of x, 1 over x, into our quotient, and f of a, 1 over a into our quotient, and that's over x minus a.
00:26
So here's the quotient that we're hoping to simplify.
00:30
And any time you have a complex fraction like this, where you have fractions inside your fraction, it's a good idea to multiply by a special form of one to clear those fractions.
00:39
So i'm going to multiply the top and bottom by x times a.
00:45
And i'm just going to put that over one so that everything lines up nicely.
00:49
So what happens then is when we multiply 1 over x by x times a, the x is cancel and we just have a minus now we multiply 1 over a by x times a and the a's cancel and we just have x...