Question 150798
Solve for x:
{{{3/(x-3) = x/(x-3)-3/2}}} Did I get this right? It helps a lot if you use parentheses, thus:
3/(3-x) = x/(3-x) - 3/2
Anyway, let's proceed.

{{{3/(x-3) = x/(x-3) - 3/2}}} Subtract the fractions on the right using 2(x-3) as the LCD
{{{3/(x-3) = (2x-3(x-3))/2(x-3)}}} Simplify the right numerator.
{{{3/(x-3) = (2x-3x+9)/2(x-3)}}}
{{{3/(x-3) = (-x+9)/2(x-3)}}} Now multiply both sides by 2.
{{{6/(x-3) = (-x+9)/(x-3)}}} so...
{{{6 = -x+9}}}
{{{x = 3}}}
However, when you try to check this solution, you'll find that you have undefined quantities:
{{{3/(x-3) = x/(x-3)-3/2}}} Substitute x = 3.
{{{3/(3-3) = 3/(3-3)-3/2}}}
{{{highlight(3/0) = highlight(3/0)-3/2}}} Division by zero is not defined in mathematics!
So, the solution is UNDEFINED.