Rational Expressions
5. Rational Expressions:
(1).Def:A rational expression is the quotient of two polynomials.
Example: ![](./articles_imgs/6159/ration1.jpg)
(2)Domain: the set of all real numbers for which the expression is defined.
For a rational expression, the domain is the set of the numbers that make the
denominator
nonzero.
Example:
![](./articles_imgs/6159/ration2.jpg)
so the domain of this expression is
![](./articles_imgs/6159/ration3.jpg)
(3)Simplifying, Multiplying, and Dividing rational expressions
![](./articles_imgs/6159/ration4.jpg)
Example:
![](./articles_imgs/6159/ration5.jpg)
(3)Adding and Subtracting Rational Expressions
![](./articles_imgs/6159/ration6.jpg)
Example:
![](./articles_imgs/6159/ration7.jpg)
![](./articles_imgs/6159/ration8.jpg)
* Strategy:(1)simplify. (2) find the least common
denominator (LCD)
6 : Radical Notation and Rational Exponents:
(1)n-th :![](./articles_imgs/6159/ration9.jpg)
Example: ![](./articles_imgs/6159/ration10.jpg)
(2)(i)if n is even: ![](./articles_imgs/6159/ration11.jpg)
(ii) if n is odd:![](./articles_imgs/6159/ration12.jpg)
![](./articles_imgs/6159/ration13.jpg)
Example: Simplify
![](./articles_imgs/6159/ration14.jpg)
(3):Rational Exponents:
(i) Def: , where m and n are integers
![](./articles_imgs/6159/ration16.jpg)
Example:
![](./articles_imgs/6159/ration17.jpg)
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