![]() 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. 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.
0 Comments
Leave a Reply. |
Details
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |