Question 163963
In order to add the fractions, we need to get the denominators equal to one another. So we need to get them equal to the LCD {{{(x+6)(x-6)}}}


{{{(7x)/(x+6)+3/(x-6)}}} Start with the given expression



{{{(7x(x-6))/((x+6)(x-6))+3/(x-6)}}} Multiply both the numerator and denominator of the first fraction by {{{x-6}}}



{{{(7x(x-6))/((x+6)(x-6))+(3(x+6))/((x+6)(x-6))}}} Multiply both the numerator and denominator of the second fraction by {{{x+6}}}



{{{(7x^2-42x)/((x+6)(x-6))+(3x+18)/((x+6)(x-6))}}} Distribute



{{{(7x^2-42x+3x+18)/((x+6)(x-6))}}} Add the fractions



{{{(7x^2-39x+18)/((x+6)(x-6))}}} Combine like terms



So {{{(7x)/(x+6)+3/(x-6)}}} simplifies to {{{(7x^2-39x+18)/((x+6)(x-6))}}}