This gives x = − 3 o r x = 3 x=-3 \ or \ x=3 x = − 3 o r x = 3. Using the property of zero product, x + 3 = 0 o r x − 3 = 0 x+3=0\ or \ x-3=0 x + 3 = 0 o r x − 3 = 0. The first fraction a b \frac ( x + 3 ) 7 ( x − 1 ) ⋅ x − 3 1 įind the zeros of the denominator and put restrictions at these points. This has been described in the panel below. When the division of fractions take place, the first fraction is multiplied by the reciprocal of the second one. Similarly, b and d are multiplied to give the final denominator. The numerators of the two fractions a and c are multiplied to give ac in the final expression. The letters a, b, c, and d indicate the polynomials.Ĭonsider the expression on top. The multiplication and division of rational expressions have been described above pictorially. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License. We recommend using aĪuthors: Lynn Marecek, MaryAnne Anthony-Smith, Andrea Honeycutt Mathis Use the information below to generate a citation. Then you must include on every digital page view the following attribution: If you are redistributing all or part of this book in a digital format, Then you must include on every physical page the following attribution:
If you are redistributing all or part of this book in a print format, Want to cite, share, or modify this book? This book uses the Together you can come up with a plan to get you the help you need. See your instructor as soon as possible to discuss your situation. You need to get help immediately or you will quickly be overwhelmed. …no - I don’t get it! This is critical and you must not ignore it. Is there a place on campus where math tutors are available? Can your study skills be improved? Whom can you ask for help? Your fellow classmates and instructor are good resources. It is important to make sure you have a strong foundation before you move on. Math is sequential - every topic builds upon previous work. This must be addressed quickly as topics you do not master become potholes in your road to success. What did you do to become confident of your ability to do these things? Be specific! Congratulations! You have achieved your goals in this section! Reflect on the study skills you used so that you can continue to use them. Ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section. So the rational expression a − b b − a a − b b − a simplifies to −1 −1.Įxplain all the steps you take to simplify the rational expression p 2 + 4 p − 21 9 − p 2. In general, we could write the opposite of a − b a − b as b − a b − a. This means the fraction x − 3 3 − x x − 3 3 − x simplifies to −1 −1. −1īut the opposite of x − 3 x − 3 could be written differently: So, in the same way, we can simplify the fraction x − 3 − ( x − 3 ) x − 3 − ( x − 3 ): We simplify the fraction a − a a − a, whose numerator and denominator are opposites, in this way: In Foundations, we introduced opposite notation: the opposite of a a is − a − a. We also recognize that the numerator and denominator are opposites. We know this fraction simplifies to −1 −1. Let’s start with a numerical fraction, say 7 −7 7 −7.
#Multiplying and dividing rational expressions how to
Now we will see how to simplify a rational expression whose numerator and denominator have opposite factors. Simplify Rational Expressions with Opposite Factors That way, when we solve a rational equation for example, we will know whether the algebraic solutions we find are allowed or not. So before we begin any operation with a rational expression, we examine it first to find the values that would make the denominator zero. The numerator of a rational expression may be 0-but not the denominator. If the denominator is zero, the rational expression is undefined. In order to avoid dividing by zero in a rational expression, we must not allow values of the variable that will make the denominator be zero. When we work with a numerical fraction, it is easy to avoid dividing by zero, because we can see the number in the denominator. We will simplify, add, subtract, multiply, divide, and use them in applications.ĭetermine the Values for Which a Rational Expression is Undefined We will perform the same operations with rational expressions that we do with fractions. Since a constant is a polynomial with degree zero, the ratio of two constants is a rational expression, provided the denominator is not zero.
Notice that the first rational expression listed above, − 13 42, − 13 42, is just a fraction.
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