MTH 092 — Spring — 2005
Essex County College — Division of Mathematics
Quiz # 91— March 31, 2005
Name:
Signature:
Show all work clearly and in order, and box your final answers. Justify your answers algebraically
whenever possible. You have 20 minutes to take this 10 point quiz. No calculators or cellular
phones allowed. Do two of the following three problems.
1. Simplify. x
x+ 3 +2x−1
x2+x−6
Work: The LCM is (x+ 3) (x−2).
x
x+ 3 +2x−1
x2+x−6=x
x+ 3 +2x−1
(x+ 3) (x−2)
=x
x+ 3 +2x−1
(x+ 3) (x−2)
=x
x+ 3
·
x−2
x−2+2x−1
(x+ 3) (x−2)
=x2
−2x
(x+ 3) (x−2) +2x−1
(x+ 3) (x−2)
=x2
−1
(x+ 3) (x−2)
2. Solve for x.x
x+ 3 +2x−1
x2+x−6= 0
Work: The LCM is (x+ 3) (x−2).
x
x+ 3 +2x−1
(x+ 3) (x−2) = 0
(x+ 3) (x−2) ·
x
x+ 3 + (x+ 3) (x−2) ·
2x−1
(x+ 3) (x−2) = (x+ 3) (x−2) ·0
(x−2) ·x+ (2x−1) = 0
x2
−1=0
(x−1) (x+ 1) = 0
1This document was prepared by Ron Bannon using L
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