SOLUTION: How do you solve for x when it is in both the numerator and denominator on both sides of a rational equation? And what are the restrictions for x? This is the nasty problem:

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Question 81646This question is from textbook Algebra I
: How do you solve for x when it is in both the numerator and denominator on both sides of a rational equation? And what are the restrictions for x? This is the nasty problem:
x-7/x-9 = 2/x-9 This question is from textbook Algebra I

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
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Well, you are right, it is kind of nasty!
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%28%28x-7%29%29%2F%28%28x-9%29%29 = 2%2F%28%28x-9%29%29
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You can get rid of the denominators, multiply both sides by (x-9)
Leave you with:
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x - 7 = 2
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Add 7 to both sides:
x = 2 + 7
x = 9
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However, if we substitute 9 for x, the denominators becomes (9-9)
Division by 0 is, of course, not allowed, so there is no solution
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