Question

your turn!
practice: multiply two rational expressions
which of the following is equivalent to \\(\dfrac{2}{x + 1} \cdot \dfrac{x + 1}{x + 2}\\)?
choose 1 answer:
\\(\boldsymbol{\text{a}}\\) \\(\dfrac{2}{x + 1}\\)
\\(\boldsymbol{\text{b}}\\) \\(\dfrac{2}{x + 2}\\)
\\(\boldsymbol{\text{c}}\\) \\(\dfrac{x + 3}{2x + 3}\\)
\\(\boldsymbol{\text{d}}\\) \\(\dfrac{2x + 2}{2x + 3}\\)
check
explain

Explanation:

Step1: Multiply the numerators and denominators

To multiply two rational expressions, we multiply the numerators together and the denominators together. So, \(\frac{2}{x + 1}\cdot\frac{x + 1}{x + 2}=\frac{2(x + 1)}{(x + 1)(x + 2)}\)

Step2: Cancel out the common factor

We can see that \(x + 1\) is a common factor in the numerator and the denominator. So we cancel out \(x + 1\) (assuming \(x
eq - 1\) to avoid division by zero), and we get \(\frac{2}{x + 2}\)

Answer:

B. \(\frac{2}{x + 2}\)