Rationalizing the Denominator with Variables in the Radicand
Rationalizing the denominator with a variable in the radical is demonstrated.
Practical Problem: Finding Average Speed
Complex fractions often appear in formulas used to solve problems. A practical problem involving the rate, time, and distance formula illustrates working with complex fractions.
Shortcut for Simplifying Radicals Before and After Multiplying
To avoid having to find perfect square factors for a large number by multiplying two radicals, first look for a common factor in the radicands that can be factored, then multiply.
Adding Rational Numbers with Different Denominators
In order to add or subtract rational expressions with different denominators, the least common denominator must be found and the fractions rewritten with the same denominator.
Adding Rational Expressions with Complicated Denominators
An example of adding rational expressions that have binomials and trinomials in the denominator is illustrated.
Adding Rational Expressions with Different Denominators
Rational expressions with different denominators are added and the procedure explained.
Adding and Subtracting Rational Expressions
The rules for adding and subtracting rational expressions are similar to those for adding and subtracting rational numbers, beginning with the rule that in order to be added, rational numbers must have the same denominator. Addition examples are dem...
Additional Problem That Requires Factoring, An
A shortcut for working with rational expressions with a denominator that need to be factored is presented.
Denominator of a Simplified Expression Never Has Radicals, The
A guideline is presented: a simplified radical expression never has radicals in the denominator. An expression with a radical in the denominator, but not in the numerator, is simplified using the identity property of multiplication and the process o...
Division with a Binomial in the Numerator
Examples of simplifying radical expressions with division when numerators contains a binomial.