Question : The process of writing a rational expression in lowest terms is called : 2151561
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Fill in the blank with one of the words or phrases listed below. Not all choices will be used.
least common denominator 
simplifying 
reciprocals 
numerator 
cross products 
ratio 
proportion 
denominator 
rational expression 
domain 
complex fraction 

a/b 
a/b 
a/b 
1) A(n) _______ is an expression that can be written in the form (P/Q), where P and Q are polynomials and Q is not 0.
A) ratio
B) proportion
C) rational expression
D) complex fraction
2) In a(n) _______, the numerator or denominator or both may contain fractions.
A) proportion
B) complex fraction
C) rational expression
D) cross products
3) For a rational expression,  (a/b) = _______ = _______.
A) (a/b), (a/b)
B) (a/b), (a/b)
C) numerator, denominator
D) (a/b), (a/b)
4) A rational expression is undefined when the _______ is 0.
A) rational expression
B) denominator
C) complex fraction
D) numerator
5) The process of writing a rational expression in lowest terms is called _______.
A) simplifying
B) reciprocals
C) least common denominator
D) rational expression
6) The expressions (2x/7) and (7/2x) are called _______.
A) proportion
B) least common denominator
C) reciprocals
D) complex fraction
7) The _______ of a list of rational expressions is a polynomial of least degree whose factors include all factors of the denominators in the list.
A) reciprocals
B) complex fraction
C) least common denominator
D) rational expression
8) A(n) _______ is the quotient of two numbers.
A) denominator
B) numerator
C) least common denominator
D) ratio
9) (x/2) = (7/16) is an example of a(n) _______.
A) proportion
B) complex fraction
C) reciprocals
D) least common denominator
10) If (a/b) = (c/d), then ad and bc are called _______.
A) cross products
B) complex fraction
C) least common denominator
D) reciprocals
11) The _______ of the rational function f(x) = (1/x  3) is {xx is a real number, x ≠ 3}.
A) domain
B) complex fraction
C) numerator
D) denominator
Find the domain of the rational function.
12) g(x) = (x^{2}  25/x^{2}  15x + 54)
A) {xx is a real number and x ≠ 5, x ≠ 5}
B) {xx is a real number and x ≠ 0}
C) {xx is a real number and x ≠ 6, x ≠ 9}
D) {xx is a real number and x ≠ 6, x ≠ 9}
Provide an appropriate response.
13) For a certain computer desk, the manufacturing cost C per desk (in dollars) is
C = (200x + 4000/x)
where x is the number of desks manufactured.
a. Find the average cost per desk when manufacturing 200 desks.
b. Find the average cost per desk when manufacturing 1000 desks.
A) a. $180; b. $196
B) a. $40; b. $24
C) a. $220; b. $204
D) a. $240; b. $220
Simplify the rational expression.
14) (5x  20/2x  8)
A) 4
B) (5/2)
C)  (5/2)
D) 4
15) (4x + 3/20x^{2} + 27x + 9)
A) (4x + 5/5x + 27)
B) (4x/5x + 3)
C) (4x + 3/20x^{2} + 27x + 9)
D) (1/5x + 3)
16) (x + 5/x^{3} + 125)
A) (1/x  5)
B) (1/x^{2} + 5x + 25)
C) (1/x^{2}  25)
D) (1/x^{2}  5x + 25)
17) (2m^{3}  2m^{2}  12m/m^{2}  5m + 6)
A) 2m
B) (2m(m  3)(m + 2)/(m + 3)(m  2))
C) (2m(m + 3)/(m  3))
D) (2m(m + 2)/(m  2))
18) (ay  3a + 4y  12/ay  3a + 7y  21)
A) (a + 4/a + 7)
B) (4y  12/7y  21)
C) ((a + 4)(y  3)/(a + 7)(y + 3))
D) ((a + 4)(y + 3)/(a + 7)(y  3))
19) (q  p/p^{2}  q^{2})
A) (1/p  q)
B) (1/q  p)
C)  (1/p + q)
D) (1/p + q)
Perform the indicated operation and simplify if possible.
20) (3/x  2)⋅(4x  8)
A) 8
B) 3
C) 4
D) 12
21) (y^{2}  9y + 18/3y + 9)⋅(y + 3/4y  24)
A) (y  3/12)
B) (y  6/12)
C) (y + 3/12)
D) ((y  3)(y  6)/12(y + 6))
22) (2x/x  4)  (x + 3/x  4)
A) (x  3/x  4)
B) (3x + 3/x  4)
C) (x + 3/x  4)
D) (3x  3/x  4)
23) (7a/a^{2} + 5a + 4)  (2/a + 4)
A) (5a + 2/(a + 1)(a + 4))
B) (5a  2/(a + 1)(a + 4))
C) (5a  2/(a  1)(a + 4))
D) (5a + 2/(a  1)(a + 4))
24) (18/x^{2}  1) + (9/x + 1)
A) (9(x + 3)/x^{2}  1)
B) (9/x + 1)
C) (9/x  1)
D) (9/x^{2}  1)
25) (x^{2}  25/x^{2} + 5x) ÷ (x^{2} + 5x + 1/3x  18)
A) (3(x + 5)(x  6)/x(x^{2} + 5x + 1))
B) (3(x  5)(x  6)/x(x^{2} + 5x + 1))
C) ((x  5)(x^{2} + 5x + 1)/3x(x  6))
D) ((x + 5)(x^{2} + 5x + 1)/3x(x  6))
26) (x + 6/x^{2}  5x + 6) + (2x  5/x^{2}  2x  3)
A) 3x + 1
B) (3x + 1/2x2  7x + 3)
C) (3x^{2}  2x + 16/(x  3)(x  2)(x + 1))
D) (3x^{2}  2x + 16/(x + 3)(x + 2)(x  1))
Solve the equation.
27) (4/y) + 7 = 5
A)  2
B) 1
C)  (1/3)
D) 2
28) (7/y  8) = (5/y + 8)
A)  (4/3)
B)  8
C)  48
D) 48
29) (3/a  3) = (a/a  3)  5
A) 3
B) 3
C) no solution
D) 3, 3
30) x  (10/x  1) = 6  (4x/x  1)
A) 4, 1
B) 1, 4
C) 4, 1
D) 1, 4
31) (2/x^{2}  9) = (8/x + 3)  (3/x  3)
A) 35
B) no solution
C) 7
D) 7
Simplify the complex fraction.
32) ((x^{9}/7y^{5}) /(x^{2}/y^{3}))
A) (x^{11}/7y^{8})
B) (x^{7}/y^{2})
C) (x^{7}/7y^{8})
D) (x^{7}/7y^{2})
33)
((3/y) + (5/y^{2})/(9/y^{2})  (25/y))
A) (1/3y  5)
B) (3y^{2} + 5/9  25y)
C) (1/3  5y)
D) (3y + 5/9  25y)
34) ((3/a) + 3/(3/a)  3)
A) (a^{2}/3  a^{2})
B) 3  a^{2}
C) (1 + a/1  a)
D) (3(1 + a)/1  a)
Solve.
35) In a sample of 75 fluorescent bulbs, 3 were found to be defective. At this rate, how many defective bulbs should be found in 525 bulbs?
A) 22
B) 23
C) 21
D) 20
36) One number plus eighteen times its reciprocal is equal to nine.
A) 3 or 6
B) 6 or 3
C) 6 or 3
D) 3 or 6
37) A boat moves 5 kilometers upstream in the same amount of time it moves 20 kilometers downstream. If the rate of the current is 9 kilometers per hour, find the rate of the boat in still water.
A) 9 km/hr
B) 15 km/hr
C) 6(2/3) km/hr
D) 3 km/hr
38) One pump can drain a pool in 12 minutes. When a second pump is also used, the pool only takes 4 minutes to drain. How long would it take the second pump to drain the pool if it were the only pump in use?
A) (1/6) min
B) 40 min
C) 3 min
D) 6 min
Given that the pair of triangles are similar, find x.
39)
A) x = 20
B) x = 19
C) x = 25
D) x = 12