Rational equation
An equation that includes one or more rational algebraic expressions.
Because denominators can become zero, rational equations often produce extraneous solutions (answers that come from algebraic steps but do not satisfy the original equation).
Extraneous solution
A value found while solving an equation algebraically that does not satisfy the original equation (often because it makes a denominator zero).
For example, in $$\frac{3}{x}=\frac{8}{x-2}$$
the restrictions are $x\neq 0$ and $x\neq 2$.
You should think of these restrictions as part of the problem statement: you are solving the equation only for allowable $x$ values.
This is often the fastest general approach.
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