SOLUTION: Consider x-8/x+5 divided by x-9/x+4.Explain why -5,9 and -4 are not allowable replacements for the varialbe x.

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Question 155252: Consider x-8/x+5 divided by x-9/x+4.Explain why -5,9 and -4 are not allowable replacements for the varialbe x.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Consider:
%28x-8%29%2F%28x%2B5%29 divided by %28x-9%29%2F%28x%2B4%29
Now any value of x that makes the denominator equal to zero is not an allowable replacement for the variable x, why, because when the denominator is zero, you are really dividing by zero and division by zero results in an undefined quantity and, thus, is not allowed.
Let's see how this works:
%28x-8%29%2F%28x%2B5%29 If x = -5, then we have %28-5-8%29%2F%28-5%2B5%29+=+%28-13%29%2F0...Division by zero - Undefined!
%28x-9%29%2F%28x%2B4%29 If x = -4, then we have %28-4-9%29%2F%28-4%2B4%29+=+%28-13%29%2F0 ...Division by zero - Undefined!
When you perfom the acual division of the two given fractions, you get:
%28%28x-8%29%2F%28x%2B5%29%29%2A%28%28x%2B4%29%2F%28x-9%29%29 If x = 9, then we have %28%289-8%29%2F%289%2B5%29%29%2A%28%289%2B4%29%2F%289-9%29%29+=+%281%2F14%29%2A%2813%2F0%29...Division by zero - Undefined!