Question

Find the sum. r/r^2-q^2 + 5/r+q​

Answer 1

Answer:

The answer is:  

$\frac{6r-5q}{r^2-q^2}$

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:

$r^2-q^2=(r+q)\,(r-q)$

the second denominator consists of only one of these factors: $(r+q)$, 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: $(r-q)$

Then we get two expressions that can be easily added as shown below:

$\frac{r}{(r+q)\,(r-q)} +\frac{5\,(r-q)}{(r+q)\,(r-q)} =\frac{r+5(r-q)}{(r+q)(r-q)} =\frac{r+5r-5q}{(r+q)\,(r-q)} =\frac{6r-5q}{r^2-q^2}$