Evaluating a Rational Expression
The method of substituting a value for the variables in a rational expression is called evaluating an expression.
Examples of Rationalizing the Denominator
Problems involving rationalizing the denominator are presented and a shortcut is given.
Examples of Division Problems with Radicals
Two division problems with radicals are demonstrated.
Multiplying then Simplifying Two Radicals
The procedure for simplifying radicals by beginning with multiplication is demonstrated.
Simplifying Complex Fractions
Simplifying a complex fraction results in a single rational expression. Two approaches to simplifying a complex fraction are demonstrated.
Using a Quadratic Equation to Calculate What Size Driveway Will Fit Within the Budget
Using the quadratic equation to solve a practical problem that involves finding calculating the width and length a driveway can be given a budgeted amount of money.
Using Factoring to Solve an Equation
An equation is presented for solution in which factoring must be used. The solution is detailed and checked.
Dividing a Radical by a Whole Number
A radical can only be divided by another radical. In the examples demonstrated, the only radical is in the numerator. The radical simplified and the fraction reduced.
Working With the Discriminant First
Work with the discriminant first because it determines whether or not the equation has a solution. If the discriminant is positive, the equation has two solutions. If the discriminant is negative, the equation has not solution. Examples of both are ...
Writing Expressions in Their Simplest Form
A simplified expression is one in which each base is written only once, there are no negative exponents, and no parentheses. Simplifying an expression makes it easier to solve complex problems, and using the rules for exponents makes simplifying exp...