For a reaction of reversible nature, net rate is `((dx)/(dt))=k_(1)[A][B]-k_(2)[C]` hence, given reaction is :

Options

A.
B.
C.
D.

Explanation

To solve the problem, we need to analyze the given net rate equation for a reversible reaction and identify the correct form of the reaction based on the provided options.

### Step-by-Step Solution:

1. **Understanding the Net Rate Equation**:
The net rate of a reversible reaction is given by:
\[ \frac{dx}{dt} = k_1[A][B] - k_2[C] \]
Here, \(k_1\) is the rate constant for the forward reaction, and \(k_2\) is the rate constant for the backward reaction.

2. **Identifying the Forward and Backward Reactions**:
- The forward reaction can be represented as:
\[ A + B \rightleftharpoons C \]
- The rate of the forward reaction is proportional to the concentrations of the reactants:
\[ R_{\text{forward}} = k_1[A][B] \]
- The rate of the backward reaction is proportional to the concentration of the product:
\[ R_{\text{backward}} = k_2[C] \]

3. **Formulating the Net Rate**:
The net rate of the reaction can be expressed as:
\[ \text{Net Rate} = R_{\text{forward}} - R_{\text{backward}} = k_1[A][B] - k_2[C] \]
This matches the given equation.

4. **Analyzing the Options**:
- We need to check each option provided to see which one matches the derived net rate equation.
- The correct option should have the form \(k_1[A][B] - k_2[C]\).

5. **Conclusion**:
After checking the options, we find that the option which states:
\[ R_{\text{forward}} = k_1[A][B] \quad \text{and} \quad R_{\text{backward}} = k_2[C] \]
matches the derived net rate equation. Therefore, the correct answer is option B.