Operations on Algebraic Fractions

Basic Operations on Algebraic Fractions

Operations with rational numbers and rational algebraic expressions are very similar. A rational number can be expressed as the quotient of two integers. A rational algebraic expression can be expressed as the quotient of two polynomials. In either case, the denominator can never be 0.

Rational Numbers:

Rational Algebraic Expressions: $\frac{5}{x},\frac{y}{10},\frac{2x}{x-5},\frac{y^2-36}{y+6},\frac{x^2-6x+5}{5x}$$\frac{5}{x}, \frac{y}{10}, \frac{2x}{x-5}, \frac{y^{2}-36}{y+6}, \frac{x^{2}-6x+5}{5x}$

If P and Q are any two algebraic expressions then $\frac{P}{Q}$$\frac{P}{Q}$ is called an algebraic fraction, where $Q \neq 0$ e.g., $\frac{a-b}{a^2+2ab+b^2}$$\frac{a-b}{a^{2}+2ab+b^{2}}$

To write a fraction in simplest form, we divide both the numerator and denominator by their greatest common factor (GCD).

Addition of Algebraic Expressions

Algebraic expressions can be added as explained in the following examples.

Example: Add the following expressions.

Solution:

(i) $\frac{x^2-1}{2}+\frac{4(2x^2-x+1)}{3}$$\frac{x^{2} - 1}{2} +\frac{4(2x^{2} - x + 1)}{3}$