Rational Expressions that Equal - 1
Rational expressions that equal -1 are recognizable: the terms in the numerator are identical to the terms in the denominator except for their signs, which are opposite.
Subtraction Problem That Requires Factoring, A
Solving a problem in which both denominators are quadratic trinomials is demonstrated.
Solving an Equation with the Least Common Denominator: Another Practice Problem
A problem is presented to practice solving an equation using the least common denominator to get a quadratic equation.
Practical Problem: How Much Land to Buy
A practical problem involving the purchase of land is presented. The available information is organized into a table, an equation is written, then solved using the least common denominator to get a quadratic equation, and the solution checked.
Factoring a Denominator to Add Rational Expressions
The process of working with a rational expression that contains a quadratic trinomial in the denominator is illustrated.
Multiplying by the Least Common Denominator to Get a Quadratic Equation
The steps involved in solving an equation by multiplying by the least common denominator to get a quadratic equation and checking the solution are detailed.
Solving an Equation with the Least Common Denominator: Practice Problem
A problem is presented to practice solving an equation using the least common denominator to get a quadratic equation.
Practical Problem: Machines Working at Different Speeds
The procedure for developing an equation to solve a practical work problem involving machines working at different speeds is detailed. The unknown is identified and an equation is written, solved, and checked.
Practical Problem: Runners' Rate of Speed
The rate, time, and distance formula is used to solve a practical problem involving runners' rate of speed.
Examples of Quadratic Equations
Quadratic equations can have one or two variables, but in simplest form all quadratic equations have exactly one variable raised to the second power. Examples of quadratic equations are presented.