Please provide me a example of Rational Equation

A **rational equation** is an equation that involves at least one rational expression, which is a fraction where the numerator and/or denominator are polynomials.

### Example of a Rational Equation:
\[
\frac{2x + 3}{x - 1} = \frac{5}{x + 2}
\]

### How to Solve It:
1. **Find a common denominator** (optional, depending on the solving method).
2. **Eliminate the fractions** by multiplying both sides of the equation by the common denominator.
3. **Solve the resulting polynomial equation.**
4. **Check for extraneous solutions** by substituting back into the original equation, ensuring no denominators are zero.

Would you like me to solve this equation in detail?

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Here are five related questions:
1. What are extraneous solutions in rational equations?
2. How do you determine the least common denominator (LCD) in rational equations?
3. What happens if the denominator of a rational equation is zero?
4. Can rational equations have no solutions?
5. What real-life situations can be modeled by rational equations?

**Tip:** Always check for restrictions in the variable that make any denominator equal to zero before solving the equation.

Explore an example of a rational equation involving fractions and polynomials. Learn how to solve the equation step-by-step, including finding a common denominator and checking for extraneous solutions. Suitable for students in Grades 10-12.

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