College Algebra / Unit 3 Alg 140 worked example, 60 to 90 seconds
Solving a Rational Equation
The idea
Solving a rational equation means noting the excluded values, clearing denominators with the LCD, solving the cleared equation, and checking every answer in the original.
In practice
Solve 1/x + 1/2 = 3/4. Excluded value: x = 0. The LCD is 4x; multiplying every term gives 4 + 2x = 3x, so x = 4. Check in the original: 1/4 + 1/2 = 3/4 — true, and 4 is not excluded, so it stands. Now the cautionary run: x/(x − 2) = 2/(x − 2) clears to x = 2, but 2 is the excluded value itself — the cleared equation offered an answer the original forbids. Write no solution, not x = 2 — the audit outranks the algebra that produced it.
Where people slip
List the excluded values before clearing; afterward they hide.
Your place on the trail
Every lesson rests on earlier ones and opens later ones. Tap any to jump.
Builds on
- Nothing. This is a starting point.
Unlocks
- Nothing yet depends on this.
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