Answer:
Sum [tex]\Rightarrow \dfrac{5x-12}{(x+3)(x-3)}[/tex]
D is correct
Step-by-step explanation:
Given: [tex]\dfrac{3}{x^2-9}+\dfrac{5}{x+3}[/tex]
We are given a rational expression and to add the expression.
First we make common denominator and then we add them
Multiply and divide the second fraction by x-3
[tex]\Rightarrow \dfrac{3}{x^2-9}+\dfrac{5(x-3)}{(x-3)(x+3)}[/tex]
[tex]\Rightarrow \dfrac{3}{x^2-9}+\dfrac{5x-15}{x^2-9}[/tex]
Now we have common denominator and write as common
[tex]\Rightarrow \dfrac{3+5x-15}{x^2-9}[/tex]
[tex]\Rightarrow \dfrac{5x-12}{x^2-9}[/tex]
Factor the denominator: [tex]a^2-b^2=(a-b)(a+b)[/tex]
[tex]\Rightarrow \dfrac{5x-12}{(x+3)(x-3)}[/tex]
Hence, The sum is [tex]\Rightarrow \dfrac{5x-12}{(x+3)(x-3)}[/tex]
