Question

what is the simplest form of the expression below?
\\(\frac{f^2 - 25}{5} \times \frac{f}{f - 5}\\)
\\(\circ\\) a. \\(f^2 + f\\)
\\(\circ\\) b. \\(\frac{f^2 + 5f}{5}\\)
\\(\circ\\) c. \\(\frac{f^2 - 25f}{5f - 5}\\)
\\(\circ\\) d. \\(\frac{f^2}{-1}\\)

Explanation:

Step1: Factor the numerator

Notice that \( f^2 - 25 \) is a difference of squares, so \( f^2 - 25=(f + 5)(f - 5) \). The expression becomes \( \frac{(f + 5)(f - 5)}{5}\times\frac{f}{f - 5} \).

Step2: Cancel common factors

Cancel out the common factor \( f - 5 \) from the numerator and the denominator. We are left with \( \frac{(f + 5)\times f}{5} \).

Step3: Simplify the numerator

Multiply out the numerator: \( \frac{f^2+5f}{5} \).

Answer:

B. \(\frac{f^{2}+5f}{5}\)