Question 190451
{{{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)))-(3/cross(2))(cross(2)(x-3))}}} Multiply EVERY term by the LCD {{{2(x-3)}}}



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



{{{6=2x-3x+9}}} Distribute and multiply



{{{6=-x+9}}} Combine like terms.



{{{6-9=-x}}} Subtract 9 from both sides



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



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



{{{x=3}}} Rearrange the terms.



So a possible solution is {{{x=3}}}, but we need to check it. So plug it back into the original equation



{{{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}}} Combine like terms.



Since division by zero is undefined, this means that {{{x=3}}} is NOT a solution (since it isn't even in the domain).



So there are no solutions.