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Algebra 2 practice

Solving Rational Equations — Practice

Clear the denominators, solve, and then check — because rational equations can produce answers that aren't really solutions.

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What you'll practice

Rational equations have variables in denominators. The method: multiply through by the least common denominator, solve what's left — and then CHECK each answer against the original denominators, because any "solution" that makes a denominator zero is extraneous and must be rejected. These questions drill the full loop, including the cases where every candidate dies.

Worked example

Solve xx−1=1x−1+2\frac{x}{x-1} = \frac{1}{x-1} + 2.

  1. Multiply every term by (x−1)(x-1): x=1+2(x−1)x = 1 + 2(x-1).
  2. Simplify: x=1+2x−2=2x−1x = 1 + 2x - 2 = 2x - 1.
  3. Solve: −x=−1-x = -1, so x=1x = 1.
  4. Check against the original: x=1x = 1 makes the denominator x−1=0x - 1 = 0 — undefined. The candidate is extraneous, so the equation has NO solution.

Common mistakes

  • Skipping the check: solving cleanly doesn't mean the answer survives — always test candidates in the original denominators.
  • Multiplying only some terms by the LCD: every term on both sides gets multiplied, including constants.
  • Rejecting a valid answer: a candidate is extraneous only if it zeroes a denominator — don't discard solutions just for being negative or fractional.

Try a few

1. Solve 5x=10x+3\frac{5}{x} = \frac{10}{x+3}.

  • x=3x = 3
  • x=−3x = -3
  • x=5x = 5
  • No solution

2. Solve 2x+13=1\frac{2}{x} + \frac{1}{3} = 1.

  • x=3x = 3
  • x=2x = 2
  • x=6x = 6
  • x=32x = \frac{3}{2}

3. Solve x+2x−2=3\frac{x+2}{x-2} = 3.

  • x=4x = 4
  • x=2x = 2
  • x=−4x = -4
  • No solution

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FAQ

What is an extraneous solution?
An answer produced by the algebra that fails in the original equation — usually by making a denominator zero. Clearing denominators can create them, which is why the final check is part of the method, not optional.
How do you solve a rational equation?
Multiply every term by the least common denominator to clear the fractions, solve the resulting equation, then check each candidate against the original denominators and reject any that make one zero.
Is Cramzoo free?
Cramzoo is free to start — every unit opens with free skills and no account is needed. This particular skill is part of Premium ($6/month or $30/year), which unlocks every skill plus the parent progress dashboard.
How is this different from IXL?
No punishing score. A wrong answer gives you a step-by-step explanation, not a number that drops — and every question is reviewed by a human before you see it.

Related Algebra 2 skills

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Start practicing — free

No login, no card. Open Algebra 2 and pick the tile.