CHAPTER 5 : RATIONAL ALGEBRAIC EXPRESSIONS
5.1 Definitions
Any algebraic expression, that is a quotient of two other algebraic expressions, is called a
rational algebraic expression. Thus if P and Q are algebraic expressions and Q  0 then the
expression
is called a rational algebraic expression.
We say that a rational algebraic expression
which the denominator Q is zero.
is meaningless for those values of the variable for
To simplify rational algebraic expressions, we may be required to factorize algebraic expressions
in the numerator and /or denominator.
Operations with algebraic fractions (i.e. rational algebraic expressions)
5.2 Reduction
To reduce an rational algebraic expression to the lowest term, first factorize the numerator and/or
denominator, then cancel the common factors.
Multiplication and division of two rational algebraic expressions
Hence to multiply together two fractions, we multiply their numerator to form a new numerator
and their denominators to form a new denominator (If you have canceled properly, your answer
will be in the reduced form)
Hence to divide one fraction by another, interchange the numerator and the denominator of the
divisor and then multiply (Note that cancellation can be done only after interchange or inversion
of the divisor).
Reduction of fractions to their lowest common denominator [Addition and Subtraction]
If P, Q, R, S are rational algebraic expressions (fractions) and Q0 , S 0 then
We first find the L.C.D. (or the L.C.M.) of the denominators and then write each fractions so as
to have this L.C.D. as a common denominator. Then add or subtract the numerators as the case
may be, and retain the common denominator. Reduce if possible.