Question 151530
A)



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



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




{{{2(3)=2(x)-(x-3)(3)}}} Simplify



{{{2(3)=2(x)-3(x-3)}}} Rearrange the terms



{{{2(3)=2(x)-3x+9}}} Distribute



{{{6=2x-3x-9}}} Multiply



{{{6-9=2x-3x}}} Subtract 9 from both sides.



{{{-3=-x}}} Combine like terms.



{{{3=x}}} Divide both sides by -1 to isolate x.



So the possible solution is {{{x=3}}}



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B)



Let's see why this possible solution is not a real solution



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



{{{(3)/(3-3)=(3)/(3-3)-(3)/(2)}}} Plug in {{{x=3}}}



{{{(3)/(0)=(3)/(0)-(3)/(2)}}} Subtract



Since division by zero is <font size=4><b>not</b></font> possible, this means that {{{x=3}}} is <font size=4><b>not</b></font> a real solution.



So this means that there are no real solutions.