SOLUTION: Explain why -5, 9, and -4 are not allowable replacements for the variable x in the following problem: x-8/x+5 divide by x-9/x+4 Help!! I don't know what to do with this one.

Algebra ->  Expressions-with-variables -> SOLUTION: Explain why -5, 9, and -4 are not allowable replacements for the variable x in the following problem: x-8/x+5 divide by x-9/x+4 Help!! I don't know what to do with this one.       Log On


   

Question 102142: Explain why -5, 9, and -4 are not allowable replacements for the variable x in the following problem:
x-8/x+5 divide by x-9/x+4
Help!! I don't know what to do with this one. Thank you very much.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28%28x-8%29%2F%28x%2B5%29%29%2F%28%28x-9%29%2F%28x%2B4%29%29 Start with the given expression



%28%28x-8%29%2F%28x%2B5%29%29%2A%28%28x%2B4%29%2F%28x-9%29%29 Multiply the first fraction by the reciprocal of the second fraction



%28%289-8%29%2F%289%2B5%29%29%2A%28%289%2B4%29%2F%289-9%29%29 Plug in x=9 (this is one of the given values)


%28%281%29%2F%2814%29%29%2A%28%2813%29%2F%280%29%29 Combine like terms. Since you cannot divide by zero, x=9 is not valid for this expression



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%28x-8%29%2F%28x%2B5%29 Now let's look at the first fraction


%28-5-8%29%2F%28-5%2B5%29 Plug in x=-5 (this is one of the given values)


%28-13%29%2F%280%29 Combine like terms. Since you cannot divide by zero, x=-5 is not valid for this expression


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%28x-9%29%2F%28x%2B4%29 Now let's look at the second fraction



%28-4-9%29%2F%28-4%2B4%29 Plug in x=-4 (this is one of the given values)


%28-13%29%2F%280%29 Combine like terms. Since you cannot divide by zero, x=-4 is not valid for this expression


So essentially, all 3 of these x values produce denominators of zero. This means they produce undefined results