Bunuel wrote:
Which of the following is equivalent to for all values of x for which both \(\frac{2x^2(x + 3) -2x -6}{x^2 + 2x - 3}\) expressions are defined?
(A) 2x^2 - 2
(B) 2x + 2
(C) x + 1
(D) 2x + 6
(E) x - 1
STRATEGY: Upon reading any GMAT Problem Solving question, we should always ask, Can I use the answer choices to my advantage?
In this case, we can easily plug in values of x to test for equivalency.
Now let's give ourselves up to 20 seconds to identify a faster approach.
In this case, we can also apply some algebraic factoring techniques to simplify the given expression.
Since I feel both techniques are equally fast, I'm going to test for equivalency since I'm less likely to make mistakes with that technique.
Key concept: If two expressions are equivalent, they must evaluate to the same value for every possible value of x.
For example, since the expression 2x + 3x is equivalent to the expression 5x, the two expressions will evaluate to the same number for every value of x.
So, if x = 7, the expression 2x + 3x = 2(7) + 3(7) = 14 + 21 = 35, and the expression 5x = 5(7) = 35Let's evaluate the given expression for \(x = 0\).
We get: \(\frac{2x^2(x + 3) -2x -6}{x^2 + 2x - 3}=\frac{2(0)^2(0 + 3) -2(0) -6}{(0)^2 + 2(0) - 3}=\frac{-6}{-3} = 2\)
We'll now evaluate each answer choice for \(x = 0\) and eliminate those that don't evaluate to \(2\)
(A) \(2(0)^2 - 2 = -2\). Doesn't evaluate to \(2\). ELIMINATE.
(B) \(2(0) + 2 = 2\).
KEEP(C) \(0 + 1 =1\). Doesn't evaluate to \(2\). ELIMINATE.
(D) \(2(0) + 6 = 6\). Doesn't evaluate to \(2\). ELIMINATE.
(E) \(0 - 1 = -1\). Doesn't evaluate to \(2\). ELIMINATE.
Answer: B
_________________
Brent Hanneson – Creator of gmatprepnow.com
Before you spend another second preparing for the GMAT, check out my article series, Are you doing it wrong?.
You’ll learn what the GMAT actually tests, and why memorizing a ton of formulas actually makes you less effective.