When fractions with the unknown in the denominator appear in the equation, we must pay attention: a denominator can never vanish. The method therefore falls into two steps. First we find the conditions of existence (the values of the unknown that make some denominator zero and that must therefore be excluded), then we solve the equation, discarding at the end any solution that violates those conditions.
In practice it is best to factorise the numerator and denominator, so as to identify clearly the forbidden values and to be able to simplify the common factors.
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Topics: First-degree equations
Concepts: Conditions of existence · Fractional equation
Skills: Solving equations · Factorising