00:01
We are given this function f of x equals x plus 3 over x plus 1.
00:08
And we're supposed to evaluate the difference quotient f of x minus f of 1 all over x minus 1 and simplify.
00:18
All right.
00:19
Of course, i know what f of x is.
00:21
So let's evaluate f of 1.
00:24
F of 1, just put a 1 everywhere you see an x, and i end up with 4 over 2, which is 2.
00:36
So f of 1 is just 2.
00:38
All right.
00:38
So let's see what we've got.
00:40
F of x is x plus 3 over x plus 1 minus f of 1 is 2.
00:50
And i'm going to put 2 over 1.
00:52
And then i've got x minus 1 in my denominator.
00:57
Okay.
00:58
If i want to clean up that numerator and combine that, i need an x plus 1 as my denominator.
01:05
So i'm going to multiply that denominator by x plus 1, which is fine as long as i multiply the numerator by x plus 1 as well.
01:15
All right.
01:15
And i'm going to change this minus to plus a negative 2 because i'm going to distribute that negative 2.
01:24
All right.
01:25
So working still in the numerator, i've got x plus 3 minus 2x minus 2 all over x plus 1.
01:40
And then, of course, my denominator is still x minus 1.
01:45
Okay...