Question 187075
{{{2/(x+5)+6/(x-5)}}} Start with the given expression.



Take note that the LCD is {{{(x+5)(x-5)}}}



{{{(2(x-5))/((x+5)(x-5))+6/(x-5)}}} Multiply the first fraction by {{{(x-5)/(x-5)}}}



{{{(2x-10)/((x+5)(x-5))+6/(x-5)}}} Distribute



{{{(2x-10)/((x+5)(x-5))+(6(x+5))/((x+5)(x-5))}}} Multiply the second fraction by {{{(x+5)/(x+5)}}}




{{{(2x-10)/((x+5)(x-5))+(6x+30)/((x+5)(x-5))}}} Distribute



{{{(2x-10+6x+30)/((x+5)(x-5))}}} Combine the fractions.



{{{(8x+20)/((x+5)(x-5))}}} Combine like terms.



So {{{2/(x+5)+6/(x-5)=(8x+20)/((x+5)(x-5))}}} where {{{x<>-5}}} or {{{x<>5}}}