Answer:
[tex]\frac{5x-12}{(x+3)(x-3)}[/tex]
Step-by-step explanation:
We can simplify the left fraction by simplifying the denominator.
First note the formula [tex]a^2-b^2=(a+b)(a-b)[/tex]
So, we can write:
[tex]\frac{3}{x^2-9}+\frac{5}{x+3}\\=\frac{3}{(x)^2-(3)^2}+\frac{5}{x+3}\\=\frac{3}{(x-3)(x+3)}+\frac{5}{x+3}[/tex]
Now, we can do LCM and write:
[tex]\frac{3}{(x-3)(x+3)}+\frac{5}{x+3}\\=\frac{3+5(x-3)}{(x+3)(x-3)}\\=\frac{3+5x-15}{(x+3)(x-3)}\\=\frac{5x-12}{(x+3)(x-3)}[/tex]
The last answer choice is right.
