Which expression is equivalent to \( \frac{3 x}{x+1} \) divided by \( x+1 \) ? \( \begin{array}{l}\frac{3 x}{x+1} \cdot \frac{1}{x+1} \\ 0 \frac{3 x}{x+1}-\frac{1}{x+1} \\ 0 \frac{x+1}{1}=\frac{3 x}{x+1} \\ 0 \frac{x+1}{3 x} \cdot \frac{x+1}{1}\end{array} \)

To find the expression equivalent to \( \frac{3 x}{x+1} \) divided by \( x+1 \), we can rewrite the division as multiplication by the reciprocal. Thus, we have: \[ \frac{3 x}{x+1} \div (x+1) = \frac{3 x}{x+1} \cdot \frac{1}{x+1} = \frac{3 x}{(x+1)^2} \] So the correct answer is \( \frac{3 x}{(x+1)^2} \). Did you know that the concept of rational expressions like this one dates back to ancient civilizations? The Babylonians were already working with fractions over 4000 years ago! They had an impressive understanding of mathematics that laid the groundwork for modern algebra. If you're applying this in real life, think of dividing workloads or resources. For example, if you have \( 3x \) units of work and need to distribute it over \( (x+1) \) tasks, dividing by \( x+1 \) can help you find out how much work each task will take. It's a great way to distribute evenly!