00:01
In this problem, we're given the function h of x equals x squared plus 8x plus 7 divided by x squared plus 2x plus 1.
00:10
Our job is to find all real numbers x that are not in the domain of the function h of x.
00:17
So the key here is to notice that since there are no square roots or even roots to worry about, the only problem we have to worry about will be when the denominator of h of x is zero.
00:30
So we have a problem, if you will, if that denominator is zero.
00:42
So let's set the denominator equal to zero and then we will eliminate all the x's that satisfy that equation.
00:55
So for that equation, we will factor.
00:58
We can use the quadratic formula or factor.
01:00
This one turns out to factor into x plus 1 times x plus 1.
01:07
So in particular, we have x plus 1 squared equals zero.
01:13
Well, the only way that x plus 1 squared can be zero for a real number x is if x plus 1 itself is zero...