Rational equations, with those messy fractions and variables in the denominator, look like a nightmare. But there's a trick to kill the fractions instantly.

The Goal: To eliminate the denominators and turn this into a simple equation you already know how to solve.

The Weapon: The Least Common Denominator (LCD).

Step 1: Find the LCD of all the fractions in your equation.

Step 2: The Killing Blow. Multiply BOTH sides of the entire equation by the LCD.

Step 3: The Magic. When you distribute the LCD to each term, every single denominator will cancel out perfectly.

You are now left with a simple polynomial or linear equation, with no fractions in sight.

Step 4: Solve this new, simpler equation for x.

Step 5: The Danger! You must check your answers. Any solution that would make one of the *original* denominators equal to zero is an 'extraneous solution' and must be thrown out.

This method transforms the ugliest problems in algebra into manageable ones. Find the LCD and destroy the fractions.