Algebra 2 Rational Equations
posted by Josh on .
What is the solution set of the equation?
I know the answer is {1} I just don't know how to get there.
X^216 x3
 =  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

X4=x3(x+2)
Common den is x+2
On the first factor out x+4 
(x^216)/(x+4)(x+2)  (x3)/(x+2) + 1 = 0
place all over a common denominator (x+4)(x+2)
(x^216)  (x3)(x+2) + (x+4)(x+2)
 = 0
(x+4)(x+2)
(x^216x^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