Question 150778
{{{(3x)/(x-1)+(6x-9)/(x-1)-6=0}}} Start with the given equation.



{{{cross((x-1))((3x)/cross((x-1)))+cross((x-1))((6x-9)/cross((x-1)))+(x-1)(-6)=(x-1)(0)}}} Multiply <font size="4"><b>every</b></font> term on both sides by the LCD {{{(x-1)}}}. Doing this will eliminate all of the fractions.



{{{3x+6x-9-6(x-1)=0}}} Simplify.




{{{3x+6x-9-6x+6=0}}} Distribute.



{{{3x-3=0}}} Combine like terms on the left side.



{{{3x=0+3}}} Add {{{3}}} to both sides.



{{{3x=3}}} Combine like terms on the right side.



{{{x=(3)/(3)}}} Divide both sides by {{{3}}} to isolate {{{x}}}.



{{{x=1}}} Reduce.




So {{{x=1}}} is a possible solution. However, we must check it.




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Check:


Let's test the possible solution {{{x=1}}}:




{{{(3x)/(x-1)+(6x-9)/(x-1)-6=0}}} Start with the given equation



{{{(3(1))/(1-1)+(6(1)-9)/(1-1)-6=0}}} Plug in {{{x=1}}}.



{{{(3)/(1-1)+(6-9)/(1-1)-6=0}}} Multiply



{{{(3)/(0)+(-3)/(0)-6=0}}} Subtract. Since division by zero is undefined, this means that {{{x=1}}} is <font size=4><b>not</b></font> a solution.



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Answer:


So there are no solutions.