Is this really a school question or is it just you being weird?
Well it depends. How you explained it, then it would be 79% but if there were less than one hundred people or more then this would be incorrect. this answer is only I there were 100 people voting and he had 79 of them. I hope this helps!
Answer:
The answer is:
![\frac{6r-5q}{r^2-q^2}](https://tex.z-dn.net/?f=%5Cfrac%7B6r-5q%7D%7Br%5E2-q%5E2%7D)
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)](https://tex.z-dn.net/?f=r%5E2-q%5E2%3D%28r%2Bq%29%5C%2C%28r-q%29)
the second denominator consists of only one of these factors:
, 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)](https://tex.z-dn.net/?f=%28r-q%29)
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}](https://tex.z-dn.net/?f=%5Cfrac%7Br%7D%7B%28r%2Bq%29%5C%2C%28r-q%29%7D%20%2B%5Cfrac%7B5%5C%2C%28r-q%29%7D%7B%28r%2Bq%29%5C%2C%28r-q%29%7D%20%3D%5Cfrac%7Br%2B5%28r-q%29%7D%7B%28r%2Bq%29%28r-q%29%7D%20%3D%5Cfrac%7Br%2B5r-5q%7D%7B%28r%2Bq%29%5C%2C%28r-q%29%7D%20%3D%5Cfrac%7B6r-5q%7D%7Br%5E2-q%5E2%7D)
It would take her 3 hrs and 6 mins to complete the second half. Hope this helps!