Question 143681
{{{(x-1)/(x-7)=(6)/(x-7)}}} Start with the given equation



{{{cross(x-7)((x-1)/cross(x-7))=cross(x-7)((6)/cross(x-7))}}} Multiply both sides by the LCD {{{x-7}}}. This will clear the fractions



{{{x-1=6}}} Simplify



{{{x=6+1}}}Add 1 to both sides



{{{x=7}}} Combine like terms on the right side




So the possible answer is {{{x=7}}} 




However, we must check our answer



Check:



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



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



{{{(6)/(0)=(6)/(0)}}} Subtract. Since division by zero is undefined (ie not possible), this means that {{{x=7}}} is <b>not</b> a solution. 





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Answer:



So there are no solutions to the equation {{{(x-1)/(x-7)=(6)/(x-7)}}}