PEAZIT Aha card
Go straight to resources ↓Rational equations: exclude zero denominators first
Multiplying by a denominator is reversible only if it is nonzero. Write excluded values before transforming.
| Expression | Meaning |
|---|---|
| 6/(x − 1) = 3; x ≠ 1 | The denominator must be nonzero. |
| 6 = 3(x − 1) | Multiply both sides by the allowed x − 1. |
| x = 3; 6/(3 − 1) = 3 | The solution satisfies the restriction and the original equation. |
One worked example
- 6/(x − 1) = 3; x ≠ 1The denominator must be nonzero.
- 6 = 3(x − 1)Multiply both sides by the allowed x − 1.
- x = 3; 6/(3 − 1) = 3The solution satisfies the restriction and the original equation.
Watch out: Substitute every solution into the original equation. An excluded value cannot become a solution.
Goal, prerequisites and card origin
What you will learn: Clear a denominator and check that the solution is allowed.
What you need first: Linear equations and rational expressions.
An original PEAZIT working card. Independent expert review and effectiveness testing have not yet taken place. · v1
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Multiplying by a denominator is reversible only if it is nonzero. Write excluded values before transforming.