Question

which expression is equivalent to \\(\frac{3x}{x + 1}\\) divided by \\(x + 1\\)?\
\\(\bigcirc\\) \\(\frac{3x}{x + 1} \cdot \frac{1}{x + 1}\\)\
\\(\bigcirc\\) \\(\frac{3x}{x + 1} + \frac{1}{x + 1}\\)\
\\(\bigcirc\\) \\(\frac{x + 1}{1} + \frac{3x}{x + 1}\\)\
\\(\bigcirc\\) \\(\frac{x + 1}{3x} \cdot \frac{x + 1}{1}\\)

Explanation:

Step1: Rewrite division as multiplication

Dividing by a term is multiplying by its reciprocal:
$$\frac{3x}{x+1} \div (x+1) = \frac{3x}{x+1} \times \frac{1}{x+1}$$

Step2: Match to given options

Compare the result to the provided choices.

Answer:

A. $\frac{3x}{x+1} \cdot \frac{1}{x+1}$