If $r(x) = 3x - 1$ And $s(x) = 2x + 1$, Which Expression Is Equivalent To $\left(\frac{r}{s}\right)(6)?$A. $\frac{3(6) - 1}{2(6) + 1}$ B. $\frac{8}{2(6) + 1}$ C. $\frac{36 - 1}{28 + 1}$ D.

Understanding the Problem

To find the equivalent expression for $\left(\frac{r}{s}\right)(6)$, we need to first understand what the notation $\left(\frac{r}{s}\right)(6)$ means. In this context, $\left(\frac{r}{s}\right)$ represents the ratio of the functions $r(x)$ and $s(x)$, and the $(6)$ indicates that we need to evaluate this ratio at $x = 6$.

Evaluating the Ratio of Functions

The ratio of functions $\left(\frac{r}{s}\right)$ can be evaluated by dividing the function $r(x)$ by the function $s(x)$. In this case, we have:

$$\left(\frac{r}{s}\right)(x) = \frac{r(x)}{s(x)} = \frac{3x - 1}{2x + 1}$$

Evaluating the Ratio at $x = 6$

Now that we have the ratio of functions, we need to evaluate it at $x = 6$. This means we need to substitute $x = 6$ into the ratio:

$$\left(\frac{r}{s}\right)(6) = \frac{3(6) - 1}{2(6) + 1}$$

Simplifying the Expression

To simplify the expression, we can evaluate the numerator and denominator separately:

$$\left(\frac{r}{s}\right)(6) = \frac{18 - 1}{12 + 1} = \frac{17}{13}$$

Comparing with the Options

Now that we have the simplified expression, we can compare it with the options:

• A. $\frac{3(6) - 1}{2(6) + 1}$
• B. $\frac{8}{2(6) + 1}$
• C. $\frac{36 - 1}{28 + 1}$
• D. (no option)

Conclusion

Based on our evaluation, the expression equivalent to $\left(\frac{r}{s}\right)(6)$ is:

$$\frac{3(6) - 1}{2(6) + 1}$$

This is option A.

Final Answer

The final answer is option A.

Understanding the Problem

To find the equivalent expression for $\left(\frac{r}{s}\right)(6)$, we need to first understand what the notation $\left(\frac{r}{s}\right)(6)$ means. In this context, $\left(\frac{r}{s}\right)$ represents the ratio of the functions $r(x)$ and $s(x)$, and the $(6)$ indicates that we need to evaluate this ratio at $x = 6$.

Q&A

Q: What is the ratio of functions $\left(\frac{r}{s}\right)$?

A: The ratio of functions $\left(\frac{r}{s}\right)$ can be evaluated by dividing the function $r(x)$ by the function $s(x)$. In this case, we have:

$$\left(\frac{r}{s}\right)(x) = \frac{r(x)}{s(x)} = \frac{3x - 1}{2x + 1}$$

Q: How do we evaluate the ratio at $x = 6$?

A: To evaluate the ratio at $x = 6$, we need to substitute $x = 6$ into the ratio:

$$\left(\frac{r}{s}\right)(6) = \frac{3(6) - 1}{2(6) + 1}$$

Q: Can we simplify the expression?

A: Yes, we can simplify the expression by evaluating the numerator and denominator separately:

$$\left(\frac{r}{s}\right)(6) = \frac{18 - 1}{12 + 1} = \frac{17}{13}$$

Q: How do we compare the simplified expression with the options?

A: We can compare the simplified expression with the options:

• A. $\frac{3(6) - 1}{2(6) + 1}$
• B. $\frac{8}{2(6) + 1}$
• C. $\frac{36 - 1}{28 + 1}$
• D. (no option)

Q: Which option is equivalent to the simplified expression?

A: Based on our evaluation, the expression equivalent to $\left(\frac{r}{s}\right)(6)$ is:

$$\frac{3(6) - 1}{2(6) + 1}$$

This is option A.

Conclusion

In this Q&A article, we have discussed the problem of finding the equivalent expression for $\left(\frac{r}{s}\right)(6)$, where $r(x) = 3x - 1$ and $s(x) = 2x + 1$. We have evaluated the ratio of functions, simplified the expression, and compared it with the options. The final answer is option A.

Final Answer

The final answer is option A.

Related Questions

• What is the ratio of functions $\left(\frac{r}{s}\right)$?
• How do we evaluate the ratio at $x = 6$?
• Can we simplify the expression?
• How do we compare the simplified expression with the options?
• Which option is equivalent to the simplified expression?

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