Rational Equations Calculator 2025: Complete Guide
Rational equations are the heart of algebra. Our Rational Equations Calculator finds the LCD, clears denominators, and checks every solution instantly with step-by-step explanations.
The 3 Core Steps
1. Find LCD: Least Common Denominator of all fractions
Example: x, x+1 → LCD = x(x+1)
2. Multiply Through: Clear every denominator
Example: 2/x + 3/(x+1) = 5 → 2(x+1) + 3x = 5x(x+1)
3. Solve & Check: Verify no division by zero
Example: x = 0.4 (valid)
Step-by-Step: 2/x + 3/(x+1) = 5
- LCD = x(x+1)
- 2(x+1) + 3x = 5x(x+1)
- 5x + 2 = 5x² + 5x
- 0 = 5x² + 3x - 2
- x = [-3 ± √49]/10 → x = 0.4
Common Mistakes to Avoid
- Forgetting to check solutions
- Using wrong LCD
- Dividing instead of multiplying
Real-World Uses
- Work-rate:
1/A + 1/B = 1/T - Parallel resistors:
1/R = 1/R1 + 1/R2 - Motion problems with fractions
FAQs
Can I use y? Yes — 2/y + 1/3 = 4.
Multiple variables? One per equation.
Conclusion
Our 2025 Rational Equations Calculator eliminates confusion with instant, accurate, step-by-step solutions. Enter your equation now!
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