A **rational equation** is an equation that involves at least one rational expression, which is the ratio of two polynomials. Rational equations often look like fractions with variables in the denominator. Here’s an example of a rational equation:

\[
\frac{2x + 1}{x - 3} = \frac{4x}{x + 2}
\]

### Steps to Solve a Rational Equation:
1. **Identify the LCD (Lowest Common Denominator):** Find the common denominator for all the rational expressions.
2. **Multiply through by the LCD:** This clears the denominators.
3. **Simplify and solve the resulting equation.**
4. **Check for extraneous solutions:** Any solution that makes the original denominator zero is not valid.

#### Example:
Solve the equation:
\[
\frac{2}{x+1} + \frac{3}{x-1} = 5
\]
1. **LCD**: \( (x+1)(x-1) \)
2. Multiply both sides by the LCD:
\[
2(x-1) + 3(x+1) = 5(x+1)(x-1)
\]
3. Expand and simplify:
\[
2x - 2 + 3x + 3 = 5(x^2 - 1)
\]
\[
5x + 1 = 5x^2 - 5
\]
4. Move all terms to one side:
\[
0 = 5x^2 - 5x - 6
\]
5. Solve the quadratic using factoring or the quadratic formula:
\[
x = 2, x = -\frac{3}{5}
\]
6. **Check for extraneous solutions** by plugging the solutions back into the original equation.

Would you like to go through a similar example step-by-step, or upload a specific equation you’re working on?

### Related Questions:
1. What is a rational function, and how does it differ from a rational equation?
2. How do you determine the domain of a rational equation?
3. Can rational equations have no solutions?
4. How do you solve rational equations with complex denominators?
5. What are common pitfalls when solving rational equations?

**Tip:** Always check for solutions that make the denominator zero, as these are invalid!

Learn how to solve rational equations with a step-by-step guide. This problem involves finding the lowest common denominator, clearing denominators, simplifying, and solving a quadratic equation. Suitable for students in Grades 9-12.

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