Answer:- D. [tex]\frac{5x-12}{(x+3)(x-3)}[/tex]
Explanation:-
Given expression:[tex]\frac{3}{x^2-9}+\frac{5}{x+3}[/tex]
Using identity [tex]a^2-b^2=(a+b)(a-b)[/tex], we get
[tex]=\frac{3}{(x+3)(x-3)}+\frac{5}{x+3}[/tex]
Taking L.C.M. of the denominator, we get
[tex]\frac{3+5(x-3)}{(x+3)(x-3)}=\frac{3+5x-15}{(x+3)(x-3)}[/tex]
[tex]=\frac{5x-12}{(x+3)(x-3)}[/tex]
[tex]\Rightarrow\frac{3}{x^2-9}+\frac{5}{x+3}=\frac{5x-12}{(x+3)(x-3)}[/tex]
Thus, D is the right option.
