Question 150906
{{{(2)/(3)=2-(5x-3)/(x-1)}}} Start with the given equation.



{{{cross(3)(x-1)((2)/cross(3))=3(x-1)(2)-3cross((x-1))((5x-3)/cross((x-1)))}}} Multiply <font size="4"><b>every</b></font> term on both sides by the LCD {{{3(x-1)}}}. Doing this will eliminate all of the fractions.




{{{2(x-1)=6(x-1)-3(5x-3)}}} Simplify.



{{{2x-2=6x-6-15x+9}}} Distribute.



{{{2x-2=-9x+3}}} Combine like terms on the right side.



{{{2x=-9x+3+2}}} Add {{{2}}} to both sides.



{{{2x+9x=3+2}}} Add {{{9x}}} to both sides.



{{{11x=3+2}}} Combine like terms on the left side.



{{{11x=5}}} Combine like terms on the right side.



{{{x=(5)/(11)}}} Divide both sides by {{{11}}} to isolate {{{x}}}.



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Answer:


So the answer is {{{x=5/11}}} 



Which approximates to {{{x=0.455}}} 



Note: if you plug in {{{x=5/11}}} back into the equation, you will get a real number (ie you won't get a division by zero). So this means that {{{x=5/11}}} 
is a solution.