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.
Verifying Right Triangles with the Pythagorean Theorem
The Pythagorean Theorem can be used to determine whether a triangle is a right triangle, given the length of its sides.
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...
More than One Base Raised to a Negative Power
The rule for raising a power to a power is applied to an expression in which a monomial in parentheses is raised to a negative power.
Using the Distance Formula to Find Distance Between Points
A practice problem is given to find the distance between coordinates using the distance formula.
Adding Rational Expressions: Practice Problem
Rational expressions with different denominators are added.