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The image you uploaded contains several equations with instructions to:

1. **Determine** whether the equation is rational, radical, or neither.  
2. **Find the excluded values** if the equation is rational.  
3. **Solve** the equation.  
4. **Classify** the equation as a contradiction, a conditional equation, or an identity.  
5. **Verify** the solution.

Let's begin with solving the first few equations:

### (a) \(\frac{3}{x-1} + \frac{2}{x+1} = \frac{7}{3x+2}\)

#### Step 1: Determine the type
This is a **rational equation** because it involves fractions with variables in the denominator.

#### Step 2: Find excluded values
We exclude values where any denominator is zero.
- \(x - 1 = 0 \Rightarrow x = 1\)
- \(x + 1 = 0 \Rightarrow x = -1\)
- \(3x + 2 = 0 \Rightarrow x = -\frac{2}{3}\)

Excluded values: \(x = 1, x = -1, x = -\frac{2}{3}\)

#### Step 3: Solve the equation
Multiply through by the least common denominator \((x - 1)(x + 1)(3x + 2)\) and simplify. Then solve for \(x\).

#### Step 4: Classification
The equation is a **conditional equation** because it has a solution, but that solution is dependent on certain values of \(x\) that don't make the equation undefined.

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Would you like me to proceed in a similar way for more of the equations, or is there a specific equation you'd like me to focus on?

Here are 5 related questions:
1. How do you solve a rational equation with multiple fractions?
2. What are the steps for determining excluded values in rational equations?
3. Can radical equations have excluded values like rational equations?
4. How can you tell if an equation is a contradiction?
5. What is the difference between an identity and a conditional equation?

**Tip**: Always check for extraneous solutions, especially when solving radical or rational equations. These can occur when squaring both sides or multiplying by an expression containing the variable.

For each equation, determine whether the equation is rational, radical, or neither of them. Explain. If it is rational, find the excluded values set. Solve the equation. Classify it as a contradiction, a conditional equation, or an identity. Verify the solution.

Learn how to identify and solve rational and radical equations. This guide covers determining excluded values, solving the equations, and classifying them as contradictions, conditional equations, or identities. Suitable for high school students in Grades 9-12.

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