Question 290748
Solve for x:
{{{(x/2)+(1/(x-1)) = x/(x-1)}}} The lowest common denominator (LCD) is: {{{2(x-1)}}}, so...
{{{(x(x-1)/2(x-1))+2/(2(x-1)) = 2x/(2(x-1))}}} Multiply through by {{{2(x-1)}}} to clear the fractions.
{{{x(x-1)+2 = 2x}}} Simplify.
{{{x^2-x+2 = 2x}}} Subtract 2x from both sides.
{{{x^2-3x+2 = 0}}} Solve by factoring.
{{{(x-1)(x-2) = 0}}} Apply the zero product rule.
{{{x-1 = 0}}} or {{{x-2 = 0}}} so...
{{{x = 1}}} or {{{x = 2}}}
However, notice that when you substitute x = 1 into the given equation, you will get undefined terms:
{{{(x/2)+(1/(x-1)) = x/(x-1)}}} Substitute x = 1.
{{{(1/2)+(1/(1-1)) = 1/(1-1)}}} or...
{{{(1/2)+1/0 = 1/0}}} but {{{1/0}}} is undefined, so x = 1 is an excluded solution.
Answer: {{{highlight(x = 2)}}}