Simplifying Rational Expressions
Simplifying rational expressions is like reducing rational numbers. First fully factor the numerator and denominator and then cancel all the common factors. The process is illustrated step by step.
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.
Rules for Working with Rational Expressions
Most of the rules for working with rational expressions are the same as the rules for working with rational numbers.
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.
Subtracting Rational Expressions
Rational expressions with the same number in the denominator are subtracted.
Solving Equations That Include Rational Expressions
To solve an equation with a rational expression, rewrite the equation to get rid of the fractions then solve the new equation. The same process is used to solve linear equations that contain rational expressions. If the solution makes any denominato...
Rational Numbers Review
In a rational number, the numerator can be any integer and the denominator can be any integer except zero. A rational expression is like a rational number. In a rational expression, the numerator and denominator can be any monomial or polynomial.
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.
Practical Problem: How Fast Can Two Workers Mow a Lawn?
A practical problem compares the rate at which two park workers mow the lawn and asks how much lawn the two can mow in an hour. The question is answered by adding rational expressions.