Algebra: Rational expressions

1 For the rational expression S = ( an+1 – 1 ) / ( a – 1), the value of S for a = 2 and n = 5 is:
A) 31
B) 127
C) 63
D) 15
E) None of the above.
2 For the rational expression in question 1 above, the value of S for a = 1 and n = 2 is:
A) 1
B) 2
C) 3
D) undefined, since the denominator of S is zero for a = 1
E) None of the above
3 For the rational expression ( x2 – 1 ) / ( x + 1)2, its reduced (simplified) expression is:
A) (x + 1) / (x – 1)
B) x + 1
C) x – 1
D) (x – 1) / (x + 1)
E) None of the above
4 For the rational expression in question 3 above, the domain of this expression is:
A) all values of x
B) all values of x satisfying x ≠ 1
C) all values of x satisfying x ≠ -1
D) all values of x satisfying x ≠ 0
E) None of the above.
5 Crystal drove 110 miles at y miles per hour. She then increased her speed by 3 miles per hour and drove an additional 150 miles. Using the equation D = RT, a rational expression for her total traveling time is:
A) 110 / y
B) 150 / (y + 3)
C) 110 / (y + 3) + 150 / y
D) 110 / y + 150 / (y + 3)
E) None of the above
6 The sum of the two rational expressions 1 / (x + 1) , 1 / (x – 1) yields:
A) x / (x2 + 1 )
B) x / (x2 – 1 )
C) 2x / (x2 + 1 )
D) 2x / (x2 – 1 )
E) None of the above
7 The domain of the rational expression resulting from the sum of the two expressions of question 6 above is:
A) all values of x
B) all values of x satisfying x ≠ 1
C) all values of x satisfying x ≠ -1
D) all values of x satisfying x ≠ 1 and x ≠ -1
E) None of the above
8 The following multiplication ( 2 + 2*sqrt(2) )(2 – 2*sqrt(2) ) yields
A) 8
B) -4
C) 4* sqrt(2)
D) 12
E) None of the above
9 Squaring the radical expression ( 2 + 2*sqrt(2) ) yields
A) 12
B) 12*sqrt(2)
C) 8*sqrt(2)
D) 12 + 8*sqrt(2)
E) None of the above.
10 1 / (2 + sqrt(2) ) is equivalent to (rationalizing the denominator)
A) ( 2 + sqrt(2) ) / 2
B) ( 2 + sqrt(2) ) / 4
C) ( 2 – sqrt(2) ) / 2
D) ( 2 – sqrt(2) ) / 4
E) None of the above