1. What Are Fractional Equations?

Fractional equations are equations that contain fractions with variables in the denominator. Solving them typically involves eliminating the fractions to simplify the equation.

2. The LCM Method

The most common method for solving fractional equations is multiplying both sides by the Least Common Multiple (LCM) of all denominators:

Key Steps:

1. Identify all denominators in the equation
2. Find the LCM of these denominators
3. Multiply every term on both sides by this LCM
4. Simplify and solve the resulting equation

3. Step-by-Step Solution

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

1. Denominators are 2 and 3
2. LCM of 2 and 3 is 6
3. Multiply all terms by 6: \(6 \times \frac{x+1}{2} + 6 \times \frac{x-1}{3} = 6 \times 1\)
4. Simplify: \(3(x+1) + 2(x-1) = 6\)
5. Expand: \(3x + 3 + 2x - 2 = 6\)
6. Combine like terms: \(5x + 1 = 6\)
7. Solve: \(5x = 5\) → \(x = 1\)

4. Using the Calculator

Tips: Enter your fractional equation using the format shown in the example. The calculator will show the solution and step-by-step working.

5. Frequently Asked Questions (FAQ)

Q1: What if my equation has variables in the denominator?
A: The LCM method still works, but you must check that solutions don't make any denominator zero (extraneous solutions).

Q2: How do I find the LCM of denominators?
A: Find the smallest number that all denominators divide into evenly. For prime numbers, multiply them together.

Q3: What if denominators have variables?
A: The LCM would include the variable factors. Multiply by the LCM and solve as normal, then check for extraneous solutions.

Q4: Can I use cross-multiplication instead?
A: Cross-multiplication works for simple proportions, but LCM is more reliable for equations with multiple fractions.

Q5: What if I get a solution that makes denominators zero?
A: Such solutions are invalid and should be discarded. Always check your solutions in the original equation.