Which of the following is equivalent to...

[AAPL]

Which of the following is equivalent to
$$\frac{\left(2x+4\right)}{2x^2+8x+8}$$
For all values of x for which both expressions are defined?

$$A.\ \frac{1}{2x^2+6}$$
$$B.\ \frac{1}{9x+2}$$
$$C.\ \frac{2}{x+6}$$
$$D.\ \frac{1}{x+4}$$
$$E.\ \frac{1}{x+2}$$

The OA is E.

I think that it is a simple question, I just need to re-write the expression, then
$$\frac{2\left(x+2\right)}{2\left(x^2+4x+4\right)}=\frac{2\left(x+2\right)}{2\left(x+2\right)^2}=\frac{1}{\left(x+2\right)}$$
And that's all, right? Is there a strategic approach to this PS question? Can any experts help, please? Thanks!

[ErikaPrepScholar]

Your approach is the best way to solve the problem. Algebraic manipulation is a common strategy on GMAT problems.

Like you mentioned, this is a relatively simple problem. If a student wasn't sure how to simplify the equation, this problem could also be solved by strategically testing numbers in each equation, but this would be much less efficient.

[Jeff@TargetTestPrep]

Which of the following is equivalent to
$$\frac{\left(2x+4\right)}{2x^2+8x+8}$$
For all values of x for which both expressions are defined?

$$A.\ \frac{1}{2x^2+6}$$
$$B.\ \frac{1}{9x+2}$$
$$C.\ \frac{2}{x+6}$$
$$D.\ \frac{1}{x+4}$$
$$E.\ \frac{1}{x+2}$$

After factoring the denominator, we can simplify the given expression:

(2x + 4)/(2x + 4)(x + 2) = 1/(x + 2)

Answer: E