# Algebraic Fractions

What are algebraic fractions?

Fractions which involve polynomial in the numerator and polynomial in the denominator are called algebraic fractions. Denominators of algebraic fractions cannot be zero. Every polynomial may be written as an algebraic fraction with denominator.

Some examples of algebraic fractions:

(i) (3x + 2)/5 is an algebraic fraction with integral denominator 5.

(ii) (11a + 7)/13 is an algebraic fraction with integral denominator 13.

(iii) 5/(x2 + 1) is an algebraic fraction with integral numerator 5.

(iv) 9/(2m2 + 5) is an algebraic fraction with integral numerator 9.

(v) (x2 + 2x + 1)/1 is an algebraic fraction with denominator 1.

(vi) (2a2 + 5a + 1)/3 is an algebraic fraction with denominator 3.

(vii) 1/(b2 + 7b + 3) is an algebraic fraction with numerator 1.

(viii) 10/(3n2 + 5n + 9) is an algebraic fraction with numerator 10.

(ix) (x + 3)/(x2 – 6x + 9) is an algebraic fraction with numerator as linear polynomial and denominator as a quadratic polynomial.

(x) (y + 15)/(5y2 + 9y + 10) is an algebraic fraction with numerator as linear polynomial and denominator as a quadratic polynomial.