freyesinsb wrote:This is a problem from the readyforGMAT.COM advanced math section. I can't seem to figure out an easy way to tackle it. Please advise. Thanks.


Which of the following is equivalent to 2x^2(x+3)-2x-6/x^2+2x-3 for all values of x for which both expressions are defined?

A.2x^2-2

B.2x+2

C.x+1

D.2x+6

E.x-1

Answer = B

Cheers,
Brent

You can also try plugging in values, but this is not always faster (it is here, though).

For example, if x=0, then we can evaluate our expression by plugging in 0 to get:
[2((0)^2)(0+3) - 2(0) - 6]/[0^2 + 2(0) - 3]
= (-6)/(-3)
= 2

So, when x=0, our expression evaluates to be 2

For an answer choice to be equivalent to the given expression, it too must evaluate to be 2.

A. 2x^2-2 = 2(0)^2 - 2 = -2 (no good - eliminate it)

B.2x+2 = 2(0) + 2 = 2 (nice - keep it)

C.x+1 = 0 + 1 = 1 (no good - eliminate it)

D.2x+6 = 2(0) + 6 = 6 (no good - eliminate it)

E.x-1 = 0 - 1 = -1 (no good - eliminate it)

So, the answer = B

Cheers,
Brent