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name: Mathematics 098 rational expressions homework due Wednesday, November 27, 2013 please show your work to get full credit for each problem 1. Simplify the expression xy if x = 2.5×10500 , y = 8×10600 , and r = 4×10−300 r2 2. For the rational expression x3 − x + 2 x+3 (notice the polynomial in the numerator is degree three ! ) (a) What is the domain of this rational expression ? (b) Simplify the rational expression by using long division or synthetic division to find the quotient & remainder (c) Check your answer using multiplication of the quotient & divisor, and then adding in the remainder. 3. For the rational expression: 2x − 5 2x − 11 − x2 − 7x + 12 x2 − 9x + 20 (a) What is the domain of this rational expression ? (b) Simplify the rational expression by calculating the difference and then reducing the result, if possible. 4. Suppose a subway agency notices that daily ridership varies inversely with the fare. If daily ridership is two million when the fare is $2, calculate the expected ridership when the fare is $2.25. 5. Suppose that the amount of radiation R is inversely proportional to the square of the distance from the source. A location 60 kilometers from the nuclear plant source experiences a radiation level at 2.09 microsieverts/hour. What would the radiation level be if the distance from the source is 84 kilometers? 6. Simplify the complex fraction: − y22 x−y 2 x2