Objective: Identify restrictions and simply rational expressions.
A rational expression is any expression that can be written as a quotient of two polynomials. Recall that a rational number is defined as any number that can be written as a quotient of two integers. Take notice of how similar the definitions of rational expressions and rational numbers are. Rational expressions are all examples of algebraic fractions. Therefore, throughout this unit we will be relying upon our rules for operations with fractions.
When working with fractions, remember that division by zero is undefined. Since rational expressions may contain variables in the denominator, there are certain values for which our variables can never be, otherwise our expression would be undefined. We call these values that make the denominator equal to zero restrictions.
Ex: 1/(x+3). If x = -3 then the expression would be undefined. 1/(-3+3) = 1/0 = undefined. Therefore -3 is called a restriction on the expression.
To learn more about restrictions and how to find restrictions for all rational expressions, watch the video below.
Since rational expressions are examples of algebraic fractions, we must learn how to simply rational expressions, just like we would with any other fraction. Remember that we simplify fractions by removing common factors from the numerator and denominator. We do the same thing with rational expressions. However, with rational expressions we must factor all polynomials before we are able to determine which commons factors to remove. See the example shown, and the video demonstrates this process even more clearly.
Ex: (x+2)/(x2+5x+6) = (x+2)/(x+2)(x+3) = (x+2)/(x+2)(x+3) = 1/(x+3)
Complete the worksheet attachment below and then check your answers using the solutions attachment. Once you have completed these exercises, click the link to advance to the next lesson.