Question 125878
{{{(x-6)/(x-7)=(1)/(x-7)}}} Start with the given expression


{{{(x-6)(x-7)=x-7}}} Cross multiply



{{{x^2-13x+42=x-7}}} Foil



{{{x^2-13x+42-x+7=0}}}  Subtract x from both sides.  Add 7 to both sides. 



{{{x^2-14x+49=0}}} Combine like terms



{{{(x-7)(x-7)=0}}} Factor the left side (note: if you need help with factoring, check out this <a href=http://www.algebra.com/algebra/homework/playground/change-this-name4450.solver>solver</a>)




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 {{{(x-6)/(x-7)=(1)/(x-7)}}}



{{{(x-6)/(x-7)=(1)/(x-7)}}} Start with the original equation



{{{(7-6)/(7-7)=(1)/(7-7)}}} Plug in {{{x=7}}}



{{{(1)/(0)=(1)/(0)}}} Subtract. Since division by zero is undefined, {{{x=7}}} is <b>not</b> a solution.




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Answer:


So there are no solutions.