#ADDING RATIONAL EXPRESSIONS FULL#

That took a while, but you got through it. This rational expression is already in simplest form because the numerator and denominator have no factors in common. If possible, simplify by finding common factors in the numerator and denominator. Īdd the numerators and keep the denominator the same. You need to multiply 21 m by 5 m to get the LCD, so multiply the entire rational expression by. The second denominator is 21 m and the LCD is 105 m 2. You need to multiply 15 m 2 by 7 to get the LCD, so multiply the entire rational expression by. The first denominator is 15 m 2 and the LCD is 105 m 2. Remember that m cannot be 0 because the denominators would be 0. Now rewrite the rational expressions to each have the common denominator of 105 m 2. Use the least common multiple for your new common denominator, it will be the LCD.Ĭompare each original denominator and the new common denominator. For the variables, the most m appears is twice. 3 appears exactly once in both of the expressions, so it will appear once in the least common multiple. You can find least common denominators for rational expressions, too, and use them to add rational expressions with unlike denominators:įind the prime factorization of each denominator.įind the least common multiple. Now that you have like denominators, add the fractions: Multiply each fraction by the fractional form of 1 that will produce a denominator of 60: Now that you have found the least common multiple, you can use that number as the least common denominator of the fractions.

#ADDING RATIONAL EXPRESSIONS FULL#

Prime factorization was faster, though, because you did not have to make a chart full of multiples to find a common multiple. Look at that-you found the same least common multiple using both methods. The least common multiple of 6, 10, and 4 is 60. In this case, 3 appears once, 5 appears once, and 2 is used twice because it appears twice in the prime factorization of 4. Multiply each number the maximum number of times it appears in a single factorization. The LCM will contain factors of 2, 3, and 5. Use prime factorization to find the least common multiple of 6, 10, and 4.įirst, find the prime factorization of each denominator. This is how the method works with numbers. The other method is to use prime factorization, the process of finding the prime factors of a number. The least of these numbers will be the least common denominator. The first is to list the multiples of each number and determine which multiples they have in common. But either way works.)įinding the least common denominator is the same as finding the least common multiple of 4, 6, and 10. You focus on using the least because then there is less simplifying to do. (By the way, you can add fractions by finding any common denominator it does not have to be the least. Since the denominators are 6, 10, and 4, you want to find the least common denominator and express each fraction with this denominator before adding. Let’s look at a numeric example to start. Once again, this process is similar to the one used for adding and subtracting numeric fractions with unlike denominators. The process is just like the addition of rational expressions, except that you subtract instead of add.Īdding and Subtracting Rational Expressions with Unlike Denominatorsīefore adding and subtracting rational expressions with unlike denominators, you need to find a common denominator. To subtract rational expressions with like denominators, follow the same process you use to subtract fractions with like denominators. So when we claim that 2 x is the equivalent of, we need to state that −4 is an excluded value. In the example above, just looking at the simplified form of 2 x as a replacement for the original, the reader would have no way of knowing that a value of −4 can’t be used for x. Sometimes, when we simplify an expression, the reader looking only at the simplified answer would not realize that there are excluded values. In the problem above, the domain is all real numbers except −4, since a value of x = −4 will create a denominator of 0. The excluded values of the domain are any values of the variable(s) that result in any denominator being equal to 0.

Remember that you should also describe the domain, the set of all possible values for the variables.

Rewrite the common factor as multiplication by 1 and simplify.

Remember that x cannot be -4 because the denominators would be 0. Since the denominators are the same, add the numerators.

Adding rational expressions