Rational Expressions

Rational Expressions

Rational expressions are represented as the quotient of two algebraic expressions. Thus, they can be manipulated like fractions. The following properties of fractions can be used to deal with rational expressions:

(1) For any real numbers a and b, where b ¹ 0,

-a/b = a/-b = -(a/b)

(2) For any real numbers a and b, where b ¹ 0,

-a/-b = a/b

(3) For any real numbers a, b and k, where b ¹ 0 and k ¹ 0,

(a·k)/(b·k) = a/b

(4) For any real numbers a and b, where a ¹ b,

(a-b)/(b-a) = -1

We can use the above properties for fractions to simplify rational expressions:

EX.