Algebraic fraction and existence conditions

Algebraic fractions extend the idea of a fraction to expressions with letters: instead of two numbers we have two polynomials, one in the numerator and one in the denominator. As with numerical fractions, the denominator can never be zero.

Definition — Algebraic fraction

An algebraic fraction is the ratio of two polynomials: $\frac{A(x)}{B(x)}, \qquad B(x)\neq 0.$ The existence conditions (E.C.) are found by setting the denominator $\neq 0$.

Determining the existence conditions therefore means solving the equation $B(x)=0$ and excluding its solutions: these are the values of the variable for which the fraction is meaningless.

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Topics: Algebraic fractions
Concepts: Existence conditions · Algebraic fraction · Polynomial