Question 200158
Take note that the LCD is {{{(x+5)(x-4)}}}



{{{3/(x+5)+4/(x-4)}}} Start with the given expression.



{{{(3(x-4))/((x+5)(x-4))+4/(x-4)}}} Multiply both the numerator and denominator of the first fraction by {{{x-4}}} (to get this denominator equal to the LCD)



{{{(3x-12)/((x+5)(x-4))+4/(x-4)}}} Distribute



{{{(3x-12)/((x+5)(x-4))+(4(x+5))/((x+5)(x-4))}}}  Multiply both the numerator and denominator of the second fraction by {{{x+5}}} (to get this denominator equal to the LCD)



{{{(3x-12)/((x+5)(x-4))+(4x+20)/((x+5)(x-4))}}} Distribute



{{{(3x-12+4x+20)/((x+5)(x-4))}}} Combine the fractions. This is now possible because the denominators are equal.



{{{(7x+8)/((x+5)(x-4))}}} Combine like terms.



{{{(7x+8)/(x^2+x-20)}}} FOIL




So {{{3/(x+5)+4/(x-4)=(7x+8)/(x^2+x-20)}}}