Question 154373
{{{a/(w+a)-a/(w-a)}}} Start with the given expression



{{{((w-a)/(w-a))(a/(w+a))-a/(w-a)}}} Multiply the first fraction by {{{(w-a)/(w-a)}}}.



{{{(a(w-a))/((w-a)(w+a))-a/(w-a)}}} Combine and multiply the fractions.



{{{(aw-a^2)/((w-a)(w+a))-a/(w-a)}}} Distribute



{{{(aw-a^2)/((w-a)(w+a))-((w+a)/(w+a))(a/(w-a))}}} Multiply the second fraction by {{{(w+a)/(w+a)}}}.



{{{(aw-a^2)/((w-a)(w+a))-(a(w+a))/((w-a)(w+a))}}}Combine and multiply the fractions.




{{{(aw-a^2)/((w-a)(w+a))-(aw+a^2)/((w-a)(w+a))}}} Distribute



{{{(aw-a^2-(aw+a^2))/((w-a)(w+a))}}} Subtract the fractions by subtracting the numerators



{{{(aw-a^2-aw-a^2)/((w-a)(w+a))}}} Distribute



{{{(-2a^2)/((w-a)(w+a))}}} Combine like terms



{{{(-2a^2)/(w^2-a^2)}}} FOIL



So {{{a/(w+a)-a/(w-a)=(-2a^2)/(w^2-a^2)}}} where {{{w<>a}}} or {{{w<>-a}}}