What is Solving Rational Equations?

Equations with rational expressions

How can I study Solving Rational Equations effectively?

Start by reading the study notes and working through the examples on this page. Then use the flashcards to test your recall. Practice with the 3 problems provided, checking solutions as you go. Regular review and active practice are key to retention.

Is this Solving Rational Equations study guide free?

Yes — all study notes, flashcards, and practice problems for Solving Rational Equations on Study Mondo are free to access. No account is needed.

What course covers Solving Rational Equations?

Solving Rational Equations is part of the Algebra 2 course on Study Mondo, specifically in the Rational Expressions section. You can explore the full course for more related topics and practice resources.

Are there practice problems for Solving Rational Equations?

Yes, this page includes 3 practice problems with detailed solutions. Each problem includes a step-by-step explanation to help you understand the approach.

Solving Rational Equations

Strategy

Find the LCD of all denominators
both sides by the LCD

❓ Question:

Solve: $\frac{x}{3} = \frac{5}{2}$

Cross multiply: $2x = 3 \cdot 5$ $2x = 15$ $x = \frac{15}{2}$

❓ Question:

Solve: $\frac{1}{x} + \frac{1}{x+2} = \frac{1}{2}$

❓ Question:

Solve: $\frac{6}{x-2} = \frac{x}{x-2} + 1$

Solve $x^2 - 5x + 6 = 0$ .

LCD: $2x(x + 2)$

Multiply both sides by LCD: $2x(x + 2) \cdot \frac{1}{x} + 2x(x + 2) \cdot \frac{1}{x+2} = 2x(x + 2) \cdot \frac{1}{2}$

$2(x + 2) + 2x = x(x + 2)$ $2x + 4 + 2x = x^2 + 2x$

Use quadratic formula: $a = 1, b = -2, c = -4$ $x = \frac{2 \pm \sqrt{4 + 16}}{2} = \frac{2 \pm \sqrt{20}}{2} = \frac{2 \pm 2\sqrt{5}}{2} = 1 \pm \sqrt{5}$

Answer: $x = 1 + \sqrt{5}$ or $x = 1 - \sqrt{5}$

LCD: $x - 2$

Multiply both sides: $6 = x + (x - 2)$ $6 = x + x - 2$ $6 = 2x - 2$ $8 = 2x$ $x = 4$

Check: Does $x = 4$ make any denominator zero? $x - 2 = 4 - 2 = 2 \neq 0$ ✓

Verify: $\frac{6}{2} = \frac{4}{2} + 1$ → ✓

Answer: $x = 4$

Solving Rational Equations

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Solving Rational Equations

Strategy

Extraneous Solutions

Common Types

Example

📚 Practice Problems

1Problem 1easy

❓ Question:

2Problem 2medium

❓ Question:

3Problem 3hard

❓ Question:

⚠️ Common Mistakes: Solving Rational Equations

🌍 Real-World Applications: Solving Rational Equations

📝 Worked Example: Solving a Quadratic by Factoring

Practice Lab

Practice with Flashcards

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📌 Related Topics in Rational Expressions

❓ Frequently Asked Questions