Based on the two rational expressions given below: Find the domain of each of the rational expressions. (Identify which values of x will make the denominator zero and thus are not allowed in the domain.) Divide your first rational expression by the second one. Write the answer in lowest terms. Find and state the common denominator between the two expressions. Build up each expression so that it has the common denominator. (Remember not to do any canceling at this point since you need those extra factors for the common denominator.) Add the two rational expressions together. Factor again if possible, and present the answer in lowest terms. Incorporate the following five math vocabulary words into your discussion. Use boldfont to emphasize the words in your writing (Do not write definitions for the words; use them appropriately in sentences describing your math work.): Domain Lowest terms Opposites LCD Build up See attached example of how this assignment should be completed in WORD. Here are the two rational expressions: Document Preview: INTRUCTOR GUIDANCE EXAMPLE: Week One Discussion Cant Cancel Terms! Here are my given rational expressions to work with. 9w 5 9w2 4 5 9w 9w2 9w + 2 The first thing I need to do for this pair of rational expressions is to find out what values make the denominator zero so I know what values for w are not allowed in the domain. To do this I set each denominator equal to zero and solve for w. 9w2 4 = 0 This is a difference of squares to factor into conjugates. (3w 2)(3w + 2) = 0 Set each factor equal to zero and solve for w. 3w 2 = 0 or 3w + 2 = 0 3w = 2 or 3w = -2 Add or subtract 2 from both sides. w = 2/3 or w = -2/3 Divide each side by 3. 9w2 9w + 2 = 0 Use the ac method for factoring, where ac = 9(2) = 18 Use factor pairs -3, -6 and make -9w = -3w 6w. 9w2 3w 6w + 2 = 0 Factor by grouping. 3w(3w 1) -2(3w 1) = 0 Common binomial factor is 3w 1. (3w 1)(3w 2) = 0 Set each factor equal to zero and solve for w. 3w 1 = 0 or 3w 2 = 0 Add 1 or 2 to both sides. 3w = 1 or 3w = 2 Divide both sides by 3. w = 1/3 or w = 2/3 So the values that are excluded from the domain of these two rational expressions are w ? 1/3, 2/3, or -2/3 Now I will divide the first rational expression by the second one. I will use the same factored versions of the denominators as worked out above. 9w 5 ú 5 9w . Flip second fraction and change to multiplication. 9w2 4 9w2 9w + 2 9w 5 . (3w 1)(3w 2) Notice that 9w 5 and 5 9w are opposites (3w 2)(3w + 2) 5 9w and will cancel out leaving -1 as the result. -1(3w 1)(3w 2) 3w 2 cancels from top and bottom (3w 2)(3w + 2) Notice -1(3w 1) = 1 3w. 1 3w This is the final answer of the division because 3w 2 of course the 3w terms cannot be canceled and this expression is already in lowest terms. 9w 5 + 5 9w . Now I will add these two rational expressions. 9w2 4 9w2 9w + 2 First they need a common denominator. The LCD = (3w 2)(3w + 2)(3w 1) based on the factoring from above. The Attachments: MAT222.W1.Dis.pdf