00:01
Okay, so you're finding what's called the difference quotient, f of x plus h minus f of x over h is called the difference quotient.
00:15
Really, our goal with the difference quotient is in calculus we let h go to zero, so we need to get rid of the h that is dominating the denominator so that we don't have a division by zero.
00:27
So you were told that f of x is equal to 1 over 2x plus 9.
00:36
So f of x plus h everywhere there's an x, now there is an x plus h.
00:47
So this is 1 over 2 times x plus h plus 9.
00:54
Remember this isn't f times x plus h.
01:00
So this is 1 over 2x plus 2h plus 9.
01:14
So f of x plus h minus f of x is 1 over 2x plus 2h plus 9 minus 1 over 2x plus 9.
01:28
Minus 1 over 2x plus 9.
01:42
We need to get these to be common denominators.
01:57
So the way i can see this happening, there's multiple different ways.
02:05
I'm going to rewrite this as 2 times x plus h plus 9 over 2.
02:14
And this one is 2 times x plus 9 over 2.
02:23
Over 2.
02:31
So we can multiply it.
02:36
We can leave it without the 2...