David W. answered • 07/25/16
Experienced Prof
Special note: This problem has a couple "tricks" that we often use to disguise an easy problem and make it look hard. The goal is that students who know the material will answer the question correctly and students who don't know the material will miss the question. If the question does not correctly discriminate between those two groups of students, it is not considered a good question -- right?
Trick 1: If I saw this problem on a standardized test, I would assume that it was designed to take up time (note: some students still think that questions must be answered strictly in order, so put some time-takers near the front).
Trick 2: Don’t put the expression in simplest terms.
Problem statement: ((1/(x-1)+(1/(x-2))/(4x-6)
Simplest terms: ((1/(x-1)+(1/(x-2))/(2x-3)
Note: Distractors A and C also uses this technique.
Trick 3: Add confusion wherever possible.
This problem is really a disguised version of: ((1/a) + (1/b)) / c
((1/a) + (1/b)) / c
(b/ab + a/ab) / c
((b+a)/ab) / c
(b+a)/abc
Where:
a=x-1
b=x-2
c=2x-3
So,
(b+a)/abc
(2x-3) / ((x-1)(x-2)(2x-3))
1 / ((x-1)(x-2))
1 / (x2 -3x + 2)
1 / (2x2 - 6x + 4)
Standardized tests often have a "brick to stumble over" or a "brick wall to run into." Since test makers think that using this technique makes good tests, there are lots and lots of "test taking tips" that clearly identify the "tricks" and thus have proved to increase individual scores by a very large amount [for both good and bad students]. That's why many teachers "teach to the test."
Norbert W.
1 / ((x-1)(x-2))
1 / (x2 -3x + 2)
1 / (2x2 - 6x + 4) -> Where did the 2 come from?
07/25/16