Question 150973
{{{3/(x+2)+x/(x^2-4)}}} Start with the given expression.




{{{3/(x+2)+x/((x-2)(x+2))}}} Factor {{{x^2-4}}} to get {{{(x-2)(x+2)}}}




{{{((x-2)/(x-2))(3/(x+2))+x/((x-2)(x+2))}}} Multiply the first fraction by {{{(x-2)/(x-2)}}}



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



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



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



{{{(4x-6)/((x-2)(x+2))}}} Combine like terms.



{{{(4x-6)/(x^2-4)}}} FOIL the denominator




So {{{3/(x+2)+x/(x^2-4)}}} simplifies to {{{(4x-6)/(x^2-4)}}}