SOLUTION: find all numbers for which the rational expression is not defined" 2x-7 ______ x^2+5x-24

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Question 595680: find all numbers for which the rational expression is not defined"
2x-7
______
x^2+5x-24
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
%282x-7%29%2F%28x%5E2%2B5x-24%29
Rational expressions are undefined when one or more denominators are zero. Your expression has just one denominator. So we just have to solve:
+x%5E2%2B5x-24+=+0
Now we factor (or use the Quadratic Formula). This factors easily:
(x + 8)(x - 3) = 0
From the Zero Product Property we know that one (or more) of the factors must be zero. So:
x + 8 = 0 or x - 3 = 0
Solving these we get:
x = -8 or x = 3
These are the values that make the denominator zero so these are the values that make your expression undefined.