Question 153113

{{{(x-2)/(x)-x/(x+3)}}} Start with the given expression.



{{{((x+3)/(x+3))((x-2)/(x))-x/(x+3)}}} Multiply the 1st term {{{(x-2)/(x)}}} by {{{(x+3)/(x+3)}}}



{{{((x-2)(x+3))/(x(x+3))-x/(x+3)}}} Combine the fractions.




{{{(x^2+x-6)/(x(x+3))-x/(x+3)}}} FOIL



{{{(x^2+x-6)/(x(x+3))-(x/x)(x/(x+3))}}} Multiply the 2nd term {{{x/(x+3)}}} by {{{x/x}}}




{{{(x^2+x-6)/(x(x+3))-(x^2)/(x(x+3))}}} Combine the fractions.



{{{(x^2+x-6-x^2)/(x(x+3))}}} Subtract the fractions.



{{{(x-6)/(x(x+3))}}} Combine like terms



{{{(x-6)/(x^2+3x)}}} Distribute



So {{{(x-2)/(x)-x/(x+3)=(x-6)/(x^2+3x)}}} where {{{x<>0}}} or {{{x<>-3}}}