Algebra 2 Solving Rational Equations Step by Step

What Are Rational Equations?

A rational equation is an equation that contains one or more fractions with variables in the denominator. For example: \( \frac{2x+1}{x-3} = 5 \).

How to Solve Rational Equations

1. Find the LCD (Least Common Denominator) of all fractions.
2. Multiply every term by the LCD to eliminate fractions.
3. Solve the resulting equation (usually linear or quadratic).
4. Check for extraneous solutions ΓÇö values that make any denominator zero are not valid.

Example

Solve \( \frac{x+1}{x-2} = 3 \)

1. Multiply both sides by \( (x-2) \): \( x + 1 = 3(x-2) \)
2. Expand: \( x + 1 = 3x - 6 \)
3. Solve: \( -2x = -7 \), so \( x = 3.5 \)
4. Check: \( x = 3.5 \) does not make the denominator zero Γ£ô

Common Mistakes

• Forgetting to check for extraneous solutions
• Not multiplying every term by the LCD

Practice

Try solving rational equations on our solver to see step-by-step solutions!