Question

what is the simplest form of the expression below?
\\(\frac{3m + n}{n - 1} \times \frac{n^2 - n}{5}\\)
\\(\bigcirc\\) a. \\(\frac{3mn^2 - 3mn}{-5}\\)
\\(\bigcirc\\) b. \\(\frac{3m + n^2}{5}\\)
\\(\bigcirc\\) c. \\(\frac{3mn + n^2}{5}\\)
\\(\bigcirc\\) d. \\(\frac{3m}{5}\\)

Explanation:

Step1: Factor the numerator of the second fraction

Factor \(n^2 - n\) as \(n(n - 1)\). So the expression becomes \(\frac{3m + n}{n - 1} \times \frac{n(n - 1)}{5}\).

Step2: Cancel out the common factor

Cancel out the common factor \((n - 1)\) from the numerator and the denominator. We get \(\frac{(3m + n) \times n}{5}\).

Step3: Expand the numerator

Expand \((3m + n) \times n\) to get \(3mn + n^2\). So the simplified expression is \(\frac{3mn + n^2}{5}\).

Answer:

C. \(\frac{3mn + n^2}{5}\)