Answer:
The answer is:
[tex]\frac{6r-5q}{r^2-q^2}[/tex]
which agrees with the last answer option (D) in the list.
Step-by-step explanation:
In order to add rational expressions, we need to express them with the same denominator. Therefore we examine what factors there are in the first denominator, which happens to be a difference of squares which is readily factored out as:
[tex]r^2-q^2=(r+q)\,(r-q)[/tex]
the second denominator consists of only one of these factors: [tex](r+q)[/tex], then in order to express both rational expressions with the same common denominator, we multiply numerator and denominator of the second fraction by the factor: [tex](r-q)[/tex]
Then we get two expressions that can be easily added as shown below:
[tex]\frac{r}{(r+q)\,(r-q)} +\frac{5\,(r-q)}{(r+q)\,(r-q)} =\frac{r+5(r-q)}{(r+q)(r-q)} =\frac{r+5r-5q}{(r+q)\,(r-q)} =\frac{6r-5q}{r^2-q^2}[/tex]
