Simplifying Rational Expressions
In this page we are going to discuss about simplifying rational expressions concept . A rational expression
is an expression of the form P(x) / Q(x) over the set of real numbers and Q(x) ? 0 where P(x) and Q(x) are two
polynomials. It is the quotient of two polynomials.
For example: 3 / x2 ,
(x4 + x3 + x + 1) / (x + 6) ,
5 / (x + 8) ,
(x - 2) / (x + 2) ,
28y-3 are all rational algebraic expressions.


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How to Simplify Rational Expressions
Let's see some examples on how to simplify rational expressions -
Rational algebraic expressions P(x) / Q(x) can be reduced to its lowest
term by dividing both numerator P(x) and denominator Q(x) by the G.C.D.
of P(x) and Q(x).
Example 1:
Simplify the rational algebraic expression (5x + 20) / (8x + 32)
Solution:
(5x + 20) / (8x + 32) = 5(x + 4) / 8(x + 4)
Cancel (x + 4) term from both numerator and denominator,
(5x + 20) / (8x + 32) = 5 / 8


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Example 2:
Simplify (5x + 20) / (6x + 24)
Solution:
(5x + 20) / (6x + 24) = 5(x + 4) / 6(x + 4)
Cancel (x + 4) term from both numerator and denominator,
(5x + 20) / (6x + 24) = 5 / 6

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