Dive into the world of rational equations where balancing numerators and denominators is key to finding solutions. This quiz will test your ability to solve these equations accurately and efficiently, sharpening your mathematical prowess. Ready to prove your skills? Let’s get started!

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## Solving Rational Equations Quiz Questions Overview

### 1. What is the first step in solving the rational equation \( \frac{2x}{x-3} = \frac{4}{x+2} \)?

Cross-multiply to eliminate the fractions

Add the fractions together

Subtract \( \frac{4}{x+2} \) from both sides

Multiply both sides by \( x-3 \)

### 2. Which of the following is a solution to the rational equation \( \frac{x+1}{x-2} = 3 \)?

x = 1

x = 2

x = 5

x = -1

### 3. What must be done to the equation \( \frac{3x}{x+4} – \frac{2}{x+4} = 1 \) before solving?

Find a common denominator

Cross-multiply

Add 2 to both sides

Subtract 1 from both sides

### 4. Which of the following is NOT a valid step in solving \( \frac{5}{x+1} + \frac{3}{x-1} = 2 \)?

Cross-multiplying the entire equation

Finding a common denominator

Multiplying both sides by \( (x+1)(x-1) \)

Adding the fractions directly

### 5. What is the solution to \( \frac{2x+3}{x-1} = 4 \)?

x = 2

x = 1

x = -1

x = 3

### 6. If \( \frac{x}{x+2} = \frac{3}{5} \), what is the value of x?

x = 1

x = 2

x = 3

x = 5

### 7. What is the least common denominator (LCD) of \( \frac{2}{x+3} \) and \( \frac{5}{x-2} \)?

x+3

x-2

x+3 and x-2

(x+3)(x-2)

### 8. Which value of x is an extraneous solution for \( \frac{x+1}{x-3} = \frac{2}{x-3} \)?

x = 1

x = 2

x = 3

x = 4

### 9. What is the solution to \( \frac{x+2}{x-4} = \frac{3}{x-4} \)?

x = 1

x = 2

x = 3

x = 4

### 10. What is the solution to \( \frac{4x}{x+1} – \frac{2}{x+1} = 1 \)?

x = 1

x = 2

x = 3

x = 4

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