Multiplying and Dividing Rational Expressions — Quiz
Question 9 • Algebra: Concepts and Connections
Which expression is equivalent to the product of the fraction with numerator p plus 7 and denominator 3 and 6 over p , where p is not equal to 0 ?
Answer
A
the fraction with numerator 6 p plus 7 and denominator 3 p
B
the fraction with numerator 3 p plus 21 and denominator p
C
the fraction with numerator p plus 42 and denominator 3 p
D
the fraction with numerator 2 p plus 14 and denominator p
Explanation
The product is \(\frac{p+7}{3}\times\frac{6}{p}\). Multiply the numerators and denominators: \(\frac{6(p+7)}{3p}\). Since \(6/3=2\), this simplifies to \(\frac{2(p+7)}{p}=\frac{2p+14}{p}\), which is choice D.
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