Clear the fractions first, then solve like a regular equation. One simple trick makes these problems easy.
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Solve Now →Fractions make equations look scary, but there's a simple fix: multiply every term by the LCD (least common denominator) to eliminate all fractions at once. Then you have a regular equation.
💡 The Golden Rule
Whatever you multiply one side by, you must multiply the OTHER side by too—including every term.
For more on working with fractions in algebra, see Math is Fun's guide.
Look at all the denominators in your equation. Find their least common multiple. This is your LCD.
Example: If denominators are 2, 3, and 6
LCD = 6 (since 6 is divisible by 2, 3, and 6)
Multiply every single term on both sides by the LCD. Don't forget terms without fractions!
The LCD cancels with each denominator, leaving you with a fraction-free equation.
Now solve using standard methods (combine like terms, isolate x).
Substitute back into the original equation (with fractions) to verify.
Example 1: Simple fraction equation
Solve: x/4 + 3 = 7
Example 2: Multiple fractions
Solve: x/2 + x/3 = 5
Example 3: Fractions on both sides
Solve: (2x - 1)/3 = (x + 2)/4
Example 4: Variable in denominator (careful!)
Solve: 5/x = 2
| Denominators | LCD |
|---|---|
| 2, 4 | 4 |
| 2, 3 | 6 |
| 3, 4 | 12 |
| 2, 5 | 10 |
| 4, 6 | 12 |
| 2, 3, 4 | 12 |
Forgetting to multiply ALL terms
If you multiply x/2 by 6, you must also multiply the other side by 6. Every term!
Wrong LCD
For denominators 4 and 6, the LCD is 12 (not 24). Use the LEAST common multiple.
Forgetting to distribute after clearing
After 12·(2x-1)/3 = 4(2x-1), remember: 4(2x-1) = 8x - 4, not 8x - 1.
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