00:01
Problem 30.
00:03
Equation is 5 divided p minus 2 minus 7 divided by p plus 2 equals 12 over p squared minus 4.
00:21
Here we will use a little trick.
00:23
But first i want to say that we could use we could do the same thing as the last problem.
00:29
That is multiply everything by p minus 2, multiply everything by p minus 2, multiply.
00:34
Everything by p plus 2 and then multiply everything by p squared minus 4 and this way we would get rid of all the denominators everything would be fine it would be a lot of work a lot of math but everything will be fine here we'll use a little trick so that you get used to seeing those little tricks you can do with math the thing you have to know this in this problem is that if you factor p squared minus 4 so p squared minus 4, if you factor that, you get that it is equal to p minus 2 times p plus 2.
01:21
Right? p times p is p squared.
01:26
Then you would have p times 2 p.
01:31
I'll just do it because it's a lot of talking for not a lot of writing.
01:37
So we have p squared and then minus 2 times p is minus 2 p.
01:42
And then p plus 2 that's plus 2 p and then minus 2 times 2 that's minus 4 and those two things cancel out so that you have p squared minus 4 all right so that was the trick here that's the thing you got to notice and so we'll just rewrite this equation but using this equality 12 over p squared minus 4 is p minus 2 times p plus 2 and now the good thing is that we won't have to multiply anything by p squared minus 4, because we could express it as a combination of the other denominators out there.
02:33
All right, so what we're going to do now is we're going to multiply everything by p -minus 2 times p -plus -2 to get rid of those denominators that are really annoying.
02:58
5 times p -minus 2.
03:00
I'll just write everything down.
03:02
Let's do all the steps.
03:04
It's the first time we do it together.
03:09
Minus 7 p minus 2 p plus 2 over p plus 2 equals 12 times p minus 2 times p plus 2 over p plus 2...