The activity that starts this lesson containd some of the very large collection of fractions that we encounter every day. Fractions are always present around us and as student of mathematics, we shoukd be able to understand them and know how they work and how we interpret them.
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For this lesson, we will be studying fractions and for sure we will not be reacting the way the girk did in the comic strip. Rational expressions play a big part in algebra and are used in studying a lot of different concepts. But what makes a rational expession?
Rational Expression = In arithmetic, it is the quotient or the ratio of two numbers. = In algebra, it is the quotient of two polynomials in the form a/b, where a and b are both polynomials, and b is not equal to 0. Examples:
Simplifying Rational Expressions It is important that a rational expression is in its simplest form, just like any algebraic expressions. In order to do so, let us recall first the concept of lowest terms for fractions. As you may have noticed, rational expressions are basically fractions. This means that placing fractions in lowest terms follow the same concept as simplifying rational expressions. In reducing fractions to lowest terms, we need to determine the greatest common factor of the numerator and the denominator, or write the numerator and the denominator in prime factored form, and then apply Quotient of Powers property for exponents.
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We will follow the same concept in simplifyi g algebraic rational expressions. Let us look at the following example:
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If you can recall Lesson 1 of this chapter, we discussed about the properties of exponents. The expressions that illustrated the Quotient of Powers Propertt are basic examples of a rational expression which are simplified using the property. As for this example, we will simply treat this as placing the lowest term of the fraction together with applying the Quotient of Powers property. We the have,
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Since, by definition, rational expressions are composed of polynomials, it is imperative for us to simplify rational expressions that are less than the previous example. To simplify rational expressions that involve more than one term in the numerator or denominator, we will still use factoring. But for these cases, we will recall factoring polynomials as discussed in Chapter 1.
