Finding the Least Common Multiple/Least Common …



Any time you add or subtract with fractions you must have a _________________________________.Ex: add these polynomials:x2+x+1+x2+3-(x+2)Combining like termsAdding polynomials is a fancy way of saying ______________________________________________Ex: Add these rational expressions and simplify your answer: x2+x+13+x2+33-(x+2)35x2+2xyx2+xy+xy-2y2x2+xyAddition and Subtraction with Like DenominatorsTo add or subtract when denominators are the same, add or subtract the numerators and keep the same denominator. What do you do if the denominators are not common?Ex: 12 +13Ex: Add the rational expressions x+12 +x-1xWhat is a LCD? What does it mean?Find the least common denominator for this sum1x+x+2x+1Finding the Least Common Multiple/Least Common Denominator:Find the LCD/LCM for:15,12 b) 108,75 c) x, (x-1) d) x2+2x+1,x2-1How do we find the LCD/LCM?Least Common MultipleTo find the least common multiple (LCM) of two or more expressions:1. Find the prime factorization of each expression.2. Form a product that contains each factor the greatest number of times that it occurs in any one prime factorization.249242684851Add or subtract the following:6.2.30 89y-518y2 32044601358486.2.40 xx2+11x+30-4x2+9x+20 6.2.42 8p-7-p 13681653748~6.2.38 4xyx2-y2-x+yx-y =4xy-x2-2xy-y2x+yx-y=-(x2-2xy+y2)x+yx-y=-x-y2x+yx-y=-x-yx+y2439961-1256.2.64 x-1x2-1-xx-2+x2+2x2-x-2Ex: Consider the functionfx=3x-2x2+2x-24-x-3x2-9Find the simplified form and list all restrictions on the domain.Find f0& f(a)44519852079625To Add or Subtract Rational Expressions1. Determine the least common denominator (LCD) by finding the least common multiple of the denominators.2. Rewrite each of the original rational expressions, as needed, in an equivalent form that has the LCD. 3. Add or subtract the resulting rational expressions, as indicated.4. Simplify the result, if possible, and list any restrictions on the domain of functions.b) f0=186?3?(-4)=-14Things to remember:The LCM is the same as the LCD.How to find the LCM/LCDIn order to add fractions you must have a common denominator.Magic One’sReduce your answerDon’t multiply polynomial factors unless you have to. ................
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