Showing posts with label expression. Show all posts
Showing posts with label expression. Show all posts

Wednesday, May 1, 2013

Elementary Algebra Exam #4

Click on the 10 question exam covering topics in chapter 7 (Rational Expressions and Equations). Give yourself one hour to try all of the problems and then come back and check your answers.


Simplify (Assume all denominators are nonzero.)
Perform the operations and state the restrictions.
  
Solve.
 
  
10. The sum of the reciprocals of two consecutive odd integers is 4/3.  Set up an algebraic equation and use it to find the two integers.
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Tuesday, November 6, 2012

Complex Rational Expressions


It turns out that we have all the tools necessary to simplify complex algebraic fractions. The numerator and denominator of these rational expressions contain fractions and look very intimidating.  We will outline two methods for simplifying them.

Method 1: Obtain a common denominator for the numerator and denominator, multiply by the reciprocal of the denominator, then factor and cancel if possible.
Method 2: Multiply the numerator and denominator of the complex fraction by the LCD of all the simple fractions then factor and cancel if possible.

To illustrate what happened after we multiplied by the LCD we could add an extra step.

For the following solved problems, both methods are used. Choose whichever method feels most comfortable for you.

Simplify using method 1.                                 Simplify using method 2.
Video Examples on YouTube:



Adding and Subtracting Rational Expressions

When adding or subtracting rational expressions we will need a common denominator.
Simplify the resulting rational expression after adding or subtracting them.

Add or subtract.
If the rational expressions that we are adding or subtracting have unlike denominators then we will need to find the equivalent fractions with the same denominator. To do this multiply both the numerator and denominator of each expression by the factors needed to obtain a common denominator. To help determine the LCD, first factor the denominators.
Perform the operations and state the restrictions to the domain.
For the given functions find f(x) - g(x) and state the restrictions to the domain.
Video Examples on YouTube: