00:01
For problem 14, we are given the expression x squared minus 14x plus 49, all over x squared minus 49.
00:13
We are asked to simplify the expression and to also find the values that need to be excluded from the domain.
00:19
But first, we need to factor both our numerator and denominator.
00:24
In order to do this, you would see that we need two numbers that multiply together to give us 49, and also add together to give us negative 14.
00:31
And that would be x, just so we can see our little trick.
00:38
So we need two numbers that multiply together to give us 49, and also add together to give us negative 14.
00:44
And that would, of course, be negative 7 and negative 7.
00:48
So x minus 7 times, oops, times x minus 7.
00:57
And now we can factor our denominator.
01:00
Our denominator is, of course, the difference of two squares...