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Showing posts with label divide. Show all posts
Showing posts with label divide. 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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## Sunday, April 21, 2013

### Elementary Algebra Exam #3

Click on the 10 question exam covering topics in chapters 5 and 6. Give yourself one hour to try all of the problems and then come back and check your answers.

10. The length of a rectangle is 4 centimeters less than twice its width. The area is 96 square centimeters. Find the length and width. (Set up an algebraic equation then solve it)

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## Monday, November 19, 2012

### Multiplying and Dividing Radical Expressions

As long as the indices are the same, we can multiply the radicands together using the following property.
Since multiplication is commutative, you can multiply the coefficients and the radicands together and then simplify.

Multiply.

Take care to be sure that the indices are the same before multiplying.  We will assume that all variables are positive.

Simplify.

Divide radicals using the following property.
Divide. (Assume all variables are positive.)
Rationalizing the Denominator
A simplified radical expression cannot have a radical in the denominator.  When the denominator has a radical in it, we must multiply the entire expression by some form of 1 to eliminate it.  The basic steps follow.

Rationalize the denominator:
Multiply numerator and denominator by the 5th root of of factors that will result in 5th powers of each factor in the radicand of the denominator.
Notice that all the factors in the radicand of the denominator have powers that match the index.  This was the desired result, now simplify.
Rationalize the denominator.
This technique does not work when dividing by a binomial containing a radical.  A new technique is introduced to deal with this situation.

Rationalize the denominator:
Multiply numerator and denominator by the conjugate of the denominator.
And then simplify. The goal is to eliminate all radicals from the denominator.

Rationalize the denominator.