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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