In algebra, an algebraic fraction is a fraction whose numerator and denominator are algebraic expressions. Two examples of algebraic fractions are 3 x x 2 + 2 x − 3 {\displaystyle {\frac {3x}{x^{2}+2x-3}}} and x + 2 x 2 − 3 {\displaystyle {\frac {\sqrt {x+2}}{x^{2}-3}}} . Algebraic fractions are subject to the same laws as arithmetic fractions.
and
x
+
2
x
2
−
3
{\displaystyle {\frac {\sqrt {x+2}}{x^{2}-3}}}
. Algebraic fractions are subject to the same laws as arithmetic fractions.
A rational fraction is an algebraic fraction whose numerator and denominator are both polynomials. Thus 3 x x 2 + 2 x − 3 {\displaystyle {\frac {3x}{x^{2}+2x-3}}} is a rational fraction, but not x + 2 x 2 − 3 , {\displaystyle {\frac {\sqrt {x+2}}{x^{2}-3}},} because the numerator contains a square root function.
Terminology[edit]
because the numerator contains a square root function.
In the algebraic fraction a b {\displaystyle {\tfrac {a}{b}}} , the dividend a is called the numerator and the divisor b is called the denominator. The numerator and denominator are called the terms of the algebraic fraction.
, the dividend a is called the numerator and the divisor b is called the denominator. The numerator and denominator are called the terms of the algebraic fraction.
A complex fraction is a fraction whose numerator or denominator, or both, contains a fraction. A simple fraction contains no fraction either in its numerator or its denominator. A fraction is in lowest terms if the only factor common to the numerator and the denominator is 1.
An expression which is not in fractional form is an integral expression. An integral expression can always be written in fractional form by giving it the denominator 1. A mixed expression is the algebraic sum of one or more integral expressions and one or more fractional terms.
Rational fractions[edit] See also: Rational functionIf the expressions a and b are polynomials, the algebraic fraction is called a rational algebraic fraction[1] or simply rational fraction.[2][3] Rational fractions are also known as rational expressions. A rational fraction f ( x ) g ( x ) {\displaystyle {\tfrac {f(x)}{g(x)}}} is called proper if deg f ( x )
is called proper if
deg
f
(
x
)