Question

algebra: concepts and connections - plc
multiplying and dividing rational expressions
which expression is equivalent to the product of \\(\frac{p + 7}{3}\\) and \\(\frac{6}{p}\\), where \\(p \
eq 0\\)?
options:
\\(\frac{3p + 21}{p}\\)
\\(\frac{2p + 14}{p}\\)
\\(\frac{6p + 7}{3p}\\)
\\(\frac{p + 42}{3p}\\)

Explanation:

Step1: Write the product expression

$\frac{p+7}{3} \times \frac{6}{p}$

Step2: Multiply numerators and denominators

$\frac{(p+7) \times 6}{3 \times p}$

Step3: Simplify the constant terms

$\frac{(p+7) \times 2}{p} = \frac{2p+14}{p}$

Answer:

$\boldsymbol{\frac{2p+14}{p}}$