Question 763436: 1. Determine what values, if any, will make this rational expression undefined. Show your work.
g(x)= (x+1)/ x^2+2x-24
my guess is that it's only x=0 but I'm not sure. can you please help me? thank you.
2. Write the rational expression x(x+1)^2 (x-5)/ x(x+2)(x-5)^3 in simplest terms. Make sure to identify what values of the variable will make the denominator undefined. Show your work.
For the undefined part, I THINK that x= 0, x= -2, and x= 5 will make it undefined, but I'm not sure. Can you please explain? Thank you.
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! 1) factor the denominator and we have
g(x)= (x+1)/ x^2+2x-24 = (x+1) / (x+6)*(x-4)
so the rational expression is undefined for x = -6 or 4
2) x(x+1)^2 (x-5)/ x(x+2)(x-5)^3
cancel (x-5) from numerator and denominator and we get
x*(x+1)^2 / x*(x+2)*(x-5)^2
cancel x from numerator and denominator and we get
(x+1)^2 / (x+2)*(x-5)^2
so the rational expression is undefined for x = -2 or 5
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