Question 174265
Solve for x:
{{{(x-1)/x(x-2) = 2/3}}} Expand the denominator of the left side.
{{{(x-1)/(x^2-2x) = 2/3}}} Multiply both sides by 3.
{{{3(x-1)/(x^2-2x) = 2}}} Multiply both sides by {{{(x^2-2x)}}}
{{{3x-3 = 2(x^2-2x)}}} Expand the right side.
{{{3x-3 = 2x^2-4x}}} Subtract 3x from both sides.
{{{-3 = 2x^2-7x}}} Add 3 to both sides.
{{{2x^2-7x+3 = 0}}} Factor this quadratic equation.
{{{(2x-1)(x-3) = 0}}} Apply the zero product rule.
{{{2x-1 = 0}}} or {{{x-3 = 0}}}, so...
{{{highlight(x = 1/2)}}} or {{{highlight(x = 3)}}}