Question 188773
{{{1/(x^2-2x)+1/x=2/3}}} Start with the given equation.



{{{1/(x(x-2))+1/x=2/3}}} Factor the first denominator



{{{3cross(x(x-2))(1/(cross(x(x-2))))+3cross(x)(x-2)(1/cross(x))=cross(3)x(x-2)(2/cross(3))}}} Multiply EVERY term by the LCD {{{3x(x-2)}}} to clear the fractions.



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



{{{3+3x-6=2x^2-4x}}} Distribute



{{{3x-3=2x^2-4x}}} Combine like terms.



{{{0=2x^2-4x-3x+3}}} Get everything to one side



{{{0=2x^2-7x+3}}} Combine like terms.



{{{0=(2x-1)(x-3)}}} Factor



{{{2x-1=0}}} or {{{x-3=0}}} Set each factor equal to zero



{{{x=1/2}}} or {{{x=3}}} Solve for "x" in each case



So the solutions are {{{x=1/2}}} or {{{x=3}}}