Question 145505
{{{(16)/(x^2-16)+(2(x-4))/(x+4)}}} Start with the given expression



{{{(16)/((x+4)(x-4))+(2(x-4))/(x+4)}}} Factor {{{x^2-16}}} to get {{{(x+4)(x-4)}}}. So the LCD is {{{(x+4)(x-4)}}}



{{{(16)/((x+4)(x-4))+((x-4)/(x-4))((2(x-4))/(x+4))}}} Multiply the second fraction by {{{(x-4)/(x-4)}}}



{{{(16)/((x+4)(x-4))+(2(x-4)(x-4))/((x+4)(x-4))}}} Combine the fractions




{{{(16)/(x^2-16)+(2(x-4)(x-4))/(x^2-16)}}} Foil {{{(x+4)(x-4)}}} to get {{{x^2-16}}}



{{{(16)/(x^2-16)+(2(x^2-8x+16))/(x^2-16)}}} Foil {{{(x-4)(x-4)}}} to get {{{x^2-8x+16}}}



{{{(16)/(x^2-16)+(2x^2-16x+32)/(x^2-16)}}} Distribute



{{{((16)+(2x^2-16x+32))/(x^2-16)}}} Since the two fractions have the same denominator, this means we can combine them.



{{{(2x^2-16x+48)/(x^2-16)}}} Combine like terms



So {{{(16)/(x^2-16)+(2(x-4))/(x+4)}}} simplifies to {{{(2x^2-16x+48)/(x^2-16)}}}. 



In other words,  {{{(16)/(x^2-16)+(2(x-4))/(x+4)=(2x^2-16x+48)/(x^2-16)}}} where {{{x<>-4}}} or {{{x<>4}}}