Answer: Choice D) [tex]\frac{5x-12}{(x+3)(x-3)}[/tex]
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Work Shown:
[tex]\frac{3}{x^2-9} + \frac{5}{x+3}\\\\\frac{3}{x^2-9} + \frac{5(x-3)}{(x+3)(x-3)}\\\\\frac{3}{x^2-9} + \frac{5x-15}{x^2-9}\\\\\frac{3+5x-15}{x^2-9}\\\\\frac{5x-12}{x^2-9}\\\\\frac{5x-12}{(x+3)(x-3)}\\\\[/tex]
The idea is to get the denominators to be the same to the LCD (lowest common denominator). Note in step 2, I multiplied top and bottom by (x-3) to get this done. Then in step 3, I used the difference of squares rule to get x^2-9. Afterward, we can combine the fractions and like terms.
