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# examples of rational expressions applications

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Question:4x-3/6 - x-3/9 how do you do this show me how

Answers:For this you should know something called LCM. In arithmetic and number theory, the least common multiple (also called the lowest common multiple or smallest common multiple) of two integers a and b, usually denoted by LCM(a, b), is the smallest positive integer that is a multiple of both a and b. It is familiar from grade-school arithmetic as the "lowest common denominator" that must be determined before two fractions can be added. This definition may be extended to rational numbers a and b: the LCM is the smallest positive rational number that is an integer multiple of both a and b. (In fact, the definition may be extended to any two real numbers whose ratio is a rational number.) If either a or b is 0, LCM(a, b) is defined to be zero. The LCM of more than two integers or rational numbers is well-defined: it is the smallest number that is an integer multiple of each of them. Examples: Integer What is the LCM of 4 and 6? Multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, ... and the multiples of 6 are: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, ... Common multiples of 4 and 6 are simply the numbers that are in both lists: 12, 24, 36, 48, 60, .... So the least common multiple of 4 and 6 is the smallest one of those: 12 = 3 4 = 2 6. Rational What is the LCM of 1/3 and 2/5? The multiples of 1/3 are: 1/3, 2/3, 3/3 = 1, 4/3, 5/3, 6/3 = 2, ... and the multiples of 2/5 are: 2/5, 4/5, 6/5, 8/5, 10/5 = 2, 12/5, .... Therefore, their LCM is 2 (6 2/3 = 5 2/5) the smallest number on both lists. Note that, by definition, if a and b are two rationals (or integers), there are integers m and n such that LCM(a, b) = m a = n b. This implies that m and n are coprime; otherwise they could be divided by their common divisor, giving a common multiple less than the least common multiple, which is absurd. The above examples illustrate this fact. Applications: When adding, subtracting, or comparing vulgar fractions, it is useful to find the least common multiple of the denominators, often called the lowest common denominator, because each of the fractions can be expressed as a fraction with this denominator. For instance, 2/21 + 1/6 = 4/42 + 7/42 = 11/42 where the denominator 42 was used because it is the least common multiple of 21 and 6. Now, let us go to your question! 4x - 3/6 - x - 3/9 4x - 1/2 - x - 1/3 4x - x - 1/2 - 1/3 3x - 3/6 - 2/6 [Apply the LCM between 1/2 and 1/3] 3x - 5/6 Hope this helps! :)

Question:

Answers:2 ^ (7/3) for exemple

Question:Im having trouble figuring out what to do when the denominator of both is different, for example: 4 + 3 -------- ------------ x-2 + x+1 I know then end product is 7(x-2) ---------- (x-2)(x+1) I don't understand why the x-2 is by the 7. I'm having this problem with all adding and subtracting rational expressions, but im good at multiplying and dividing. any help?

Answers:get a common denominator [4(x+1) + 3(x-2)] / (x-2)(x+1) now distribute the numerator [4x + 4 + 3x - 6] / (x-2)(x+1) simplify the numerator [7x - 2] / (x-2)(x+1) the first bracket is in the wrong spot that you listed above

Question:I need help with these two problems, if you could give me a step by step of how to do them I would be really thankful! Thanks for the help! 1) 5/x-3 + x/x^2-9 2) x/x-1 - 4/x+2 The / means the fraction, ^ means squared. Thanks so much!!!

Answers:Use a common denominator. There is an example on the bottom of this website. http://www.purplemath.com/modules/rtnladd.htm Good luck!