SIMPLIFYING RATIONAL EXPRESSIONS
An expression of the form f(x)/g(x) where f(x) and g(x) are two polynomials over the set of real numbers and g(x) ≠ 0 is called a rational expression.
Examples :
The following steps will be useful to simplify rational expressions.
Step 1 :
Factor both numerator and denominator, if possible.
Step 2 :
Identify the common factors in both numerator and denominator.
Step 3 :
Remove the common factors found in both numerator and denominator.
The following identities can be used to factor the expressions in numerator and denominator.
(a + b)2 = a2 + 2ab + b2
(a - b)2 = a2 - 2ab + b2
a2 - b2 = (a + b)(a - b)
(a + b)3 = a3 + 3a2b + 3ab2 + b2
(a - b)3 = a3 - 3a2b + 3ab2 - b2
a3 + b3 = (a + b)(a2 - ab + b3)
a3 - b3 = (a - b)(a2 + ab + b3)
Simplify each of the following rational expressions :
Example 1 :
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Example 2 :
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Example 18 :
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