SOLUTION: Hi, Can someone assist me ont the following problem? x-6/x-7=1/x-7

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Question 125878: Hi, Can someone assist me ont the following problem?
x-6/x-7=1/x-7
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28x-6%29%2F%28x-7%29=%281%29%2F%28x-7%29 Start with the given expression

%28x-6%29%28x-7%29=x-7 Cross multiply


x%5E2-13x%2B42=x-7 Foil


x%5E2-13x%2B42-x%2B7=0 Subtract x from both sides. Add 7 to both sides.


x%5E2-14x%2B49=0 Combine like terms


%28x-7%29%28x-7%29=0 Factor the left side (note: if you need help with factoring, check out this solver)



Now set each factor equal to zero:
x-7=0 or x-7=0

x=7 or x=7 Now solve for x in each case


Since we have a repeating answer, our only possible answer is x=7



However, notice what happens when we plug in x=7 into the original equation %28x-6%29%2F%28x-7%29=%281%29%2F%28x-7%29


%28x-6%29%2F%28x-7%29=%281%29%2F%28x-7%29 Start with the original equation


%287-6%29%2F%287-7%29=%281%29%2F%287-7%29 Plug in x=7


%281%29%2F%280%29=%281%29%2F%280%29 Subtract. Since division by zero is undefined, x=7 is not a solution.



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Answer:

So there are no solutions.