### Instruction: Find the domain of the function $\frac{x+1}{x^2+6x+8}$.### Response: To find the domain of a function, I need to look for values of x that make the function undefined or invalid.
One common way a function can be undefined is if the denominator of a fraction is zero, since division by zero is not allowed.
So I need to check when the denominator of x^2+6x+8 is zero.
I can factor the denominator as (x+2)(x+4) by looking for two numbers that multiply to 8 and add to 6.
Then I can set each factor equal to zero and solve for x.
If x+2=0, then x=-2.
If x+4=0, then x=-4.
These are the values of x that make the denominator zero and the function undefined.
Therefore, I need to exclude them from the domain.
The domain of a function is the set of all possible x-values that make the function valid.
I can write the domain using interval notation or set notation.
Using interval notation, the domain is (-infinity, -4) union (-4, -2) union (-2, infinity).
Using set notation, the domain is {x | x is a real number and x is not equal to -4 or -2}.