Question 319723
{{{1/x+1/(x+3)=1/2}}} Start with the given equation.



{{{2(x+3)+2x=x(x+3)}}} Multiply EVERY term by the LCD {{{2x(x+3)}}} to clear out the fractions.



{{{2x+6+2x=x^2+3x}}} Distribute.



{{{4x+6=x^2+3x}}} Combine like terms.



{{{0=x^2+3x-4x-6}}} Get everything to one side.



{{{0=x^2-x-6}}} Combine like terms.



{{{0=(x-3)(x+2)}}} Factor.



{{{x-3=0}}} or {{{x+2=0}}} Use the zero product property.



{{{x=3}}} or {{{x=-2}}} Solve for 'x' in each equation.



So the solutions are {{{x=3}}} or {{{x=-2}}}