Question 148489
{{{(x+9)/(x^2-9)-(2)/(x-3)}}} Start with the given expression.



{{{(x+9)/((x+3)(x-3))-(2)/(x-3)}}} Factor {{{x^2-9}}} to get {{{(x+3)(x-3)}}} (use the difference of squares)



In order to add or subtract any fractions, we need to have <font size=4><b>every</b></font> denominator to be the same. So we need to have <font size=4><b>every</b></font> denominator equal to the LCD. In this case, the LCD is {{{(x+3)(x-3)}}}



{{{(x+9)/((x+3)(x-3))-((2)/(x-3))((x+3)/(x+3))}}} Multiply the second fraction by {{{(x+3)/(x+3)}}}. Doing this will make the second fraction have a denominator equal to the LCD.



{{{(x+9)/((x+3)(x-3))-(2(x+3))/((x+3)(x-3))}}} Combine the fractions



{{{(x+9)/((x+3)(x-3))-(2x+6)/((x+3)(x-3))}}} Distribute




Now that we have equal denominators, we can combine the fractions



{{{(x+9-(2x+6))/((x+3)(x-3))}}} Combine the numerators over the common denominator.



{{{(x+9-2x-6)/((x+3)(x-3))}}} Distribute



{{{(-x+3)/((x+3)(x-3))}}} Combine like terms.



{{{(-(x-3))/((x+3)(x-3))}}} Factor a -1 from the numerator.



{{{(-highlight((x-3)))/((x+3)highlight((x-3)))}}} Highlight the common terms.




{{{(-cross((x-3)))/((x+3)cross((x-3)))}}} Cancel out the common terms.



{{{(-1)/(x+3)}}} Simplify



So {{{(x+9)/(x^2-9)-(2)/(x-3)}}} simplifies to {{{(-1)/(x+3)}}}. 



In other words, {{{(x+9)/(x^2-9)-(2)/(x-3)=(-1)/(x+3)}}} where {{{x<>-3}}} or {{{x<>3}}}