# 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