00:01
In this problem, we're going to have to set up an equation.
00:03
The first piece of it says 2 divided by the difference of a number and 3.
00:08
So the numerator is going to be 2, and the denominator is going to be that difference of that number and 3.
00:14
From there, it says minus 4 divided by the number plus 3.
00:19
So we'll have minus, and then a new fraction of 4 divided by the number plus 3.
00:26
So this will be x plus 3.
00:28
And then it says it is equal to 8 times the reciprocal of the difference of a number squared and 9.
00:37
So what this will be written out is the numerator is going to be 8, and then reciprocal means it's going to be in the denominator of a number squared and then plus 9.
00:47
And by that it's a difference, so it's going to be a minus 9.
00:51
Okay, so from here what we want to do is get a common denominator, and then we can focus on the numerators only to solve it.
00:59
So we're solving a rational function.
01:01
So i see i have x minus 3.
01:03
The next one is x plus 3.
01:05
And if i were to factor x squared minus 9, this is x plus 3 times x minus 3.
01:10
So my goals here are to get it so they all have the factors of x plus 3 and x minus 3.
01:16
So for the very first fraction, i'm going to multiply them both by x plus 3 and x plus 3.
01:22
For the second one, i'm going to multiply through by x minus 3 and x minus 3.
01:27
And that third fraction, i'm not going to have to multiply by anything.
01:31
So in the first fraction, i'm going to distribute 2x plus 6.
01:36
And in the denominator, i can go ahead and foil that out.
01:39
And that gets me the x squared minus 9.
01:42
For the next piece of that minus, i'm going to multiply 4 times x minus 3...