Question

enter the correct answer in the box.
jesse is traveling up and down a stream in a kayak. he can paddle the kayak at an average rate of 5 miles/hour, and the round - trip is a total distance of 16 miles. when c is the speed of the current, this expression can be used to find the difference of the time it takes jesse to travel upstream (against the current) and downstream (with the current).
$\frac{8}{5 - c}-\frac{8}{5 + c}$
find the difference in simplest form.

Explanation:

Step1: Find a common denominator

The denominators are \(5 - c\) and \(5 + c\), so the common denominator is \((5 - c)(5 + c)\) (which is also \(25 - c^2\) by the difference of squares).
Rewrite each fraction with the common denominator:
\(\frac{8}{5 - c}=\frac{8(5 + c)}{(5 - c)(5 + c)}\) and \(\frac{8}{5 + c}=\frac{8(5 - c)}{(5 - c)(5 + c)}\)

Step2: Subtract the fractions

Now subtract the two fractions:

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Answer:

\(\frac{16c}{25 - c^2}\)