Algebraic fraction

In algebra, an algebraic fraction is a fraction whose numerator and denominator are algebraic expressions. Two examples of algebraic fractions are ${\displaystyle {\frac {3x}{x^{2}+2x-3}}}$ and ${\displaystyle {\frac {\sqrt {x+2}}{x^{2}-3}}}$. 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 ${\displaystyle {\frac {3x}{x^{2}+2x-3}}}$ is a rational fraction, but not ${\displaystyle {\frac {\sqrt {x+2}}{x^{2}-3}},}$ because the numerator contains a square root function.