00:01
For problem number 19, we are given the rational expression x squared minus 5x plus 6 all over x squared minus 2x minus 3 times x squared minus 1 all over x squared minus 4.
00:24
So the first thing that we need to do is figure out what our excluded denominator values need to be.
00:31
So we're going to take both of our denominators before we multiply and simplify and set both of those equal to 0.
00:37
So x squared minus 2, x minus 3, 0, and x squared minus 4 equals 0.
00:44
So we'll have to factor both of these.
00:46
But this will be x minus 3 times x plus 1 equals 0.
00:52
And because this is a difference of 2 squares, that would be x plus 2 times x minus 2 equals 0.
01:00
Now you can go back and watch previous problems in this section to see how or a review of factoring, but in this case, just to save time, we're just going to write out our factorizations.
01:12
So we can set both of these individually equal to zero, and that would give us x equals three, x equals negative one, x equals negative two, and x equals positive two.
01:24
So our answer for our excluded values would be x is not equal to 3, 1, negative 2, or positive 2.
01:37
And now we can multiply and simplify our expression.
01:41
So we can start by multiplying straight across, and that's just going to give us x squared minus 5x plus 6 times x squared minus 1, all over x squared minus 2x minus 2.
01:57
Times x squared minus 4 and we can simplify where we can by factoring.
02:03
So the factorization of x squared minus 5x plus 6 would be x minus 6 and x plus 1...