What is the solution set of the equation?
I know the answer is {-1} I just don't know how to get there.
X^2-16 x-3
--------- = ------- -1
(x+4)(x+2) (x+2)
Get a common denominator
Drop it
Solve the numerator
Check your answer- if the answer makes the denominator equal to 0, then drop it (excluded value)
Do not forget 1 needs a common denominator
X-4=x-3-(x+2)
Common den is x+2
On the first factor out x+4
(x^2-16)/(x+4)(x+2) - (x-3)/(x+2) + 1 = 0
place all over a common denominator (x+4)(x+2)
(x^2-16) - (x-3)(x+2) + (x+4)(x+2)
----------------------------------- = 0
(x+4)(x+2)
(x^2-16-x^2+x+6+x^2+6x+8)/(x+4)(x+2) = 0
(x^2+5x+4)/(x+4)(x+2) = 0
(x+4)(x+1)/(x+4)(x+2) = 0
(x+1)/(x+2) = 0
So, f(x) = 0 when x = -1
Note that the domain excludes x = -4 and -2