00:01
Hello, so here we're given 1 over x squared minus 3 is equal to 8 over x.
00:04
So what we can do, what's making this me a little bit tough is having these fractions.
00:08
X is in the denominator.
00:10
So if we multiply everything through, well, by x, we can kill the fraction here.
00:14
We're still going to have an x in the denominator on the left side.
00:17
So maybe we multiply everything through by x squared.
00:21
Then what is going to happen? well, so we multiply everything here by x squared.
00:26
So on the left, well, we get x squared times 1 over x squared.
00:30
We basically distribute here times two terms.
00:33
Well, that just gives us x squared over x.
00:34
It is 1.
00:35
So we get 1.
00:36
Then we get, well, x squared times negative 3 is minus 3x squared.
00:40
Okay, and that's going to be equal to while x squared times 8 over x, that's 8x squared which gives us just 8 over x.
00:48
One of these factors of x cancels with one of the x squares, leaving one more factor of x doll.
00:52
So it's going to be equal to 8x.
00:55
So now, well, we can basically set this as a quadratic.
00:58
This is going to be, if we rearrange the terms, we get a.
01:00
Negative 3x squared minus 8x plus 1 is going to be equal to 0 and now we can see that we can try to solve this by the quadratic formula therefore we get that x is going to be equal to negative b so minus a negative 8 so 8 then plus or minus the square root of negative 8 squared minus 4ac so minus 4 times negative 3 times 1 all divided by 2a so by 2 times negative 3 so if we continue here what we get we get 8 plus or minus the square root of negative 8 squared is going to be positive 64...