APPROACH #1: Scan the answer choices
Upon scanning the five answer choices, I see that D is always positive.

D. (x + y)² + 1
Since (x + y)² is greater than or equal to 0 for all values of x and y, we can be certain that (x + y)² + 1 must be positive

Answer: D

APPROACH #2: Use counter-examples to eliminate for answer choices

A. x/y
If x = -1 and y = 1, then x/y = (-1)/1 = -1, which is not positive.
Eliminate answer choice A

B. xy
If x = -1 and y = 1, then xy = (-1)(1) = -1, which is not positive.
Eliminate answer choice B

C. 2y + x
If x = -3 and y = 1, then 2y + x = 2(1) + (-3) = -1, which is not positive.
Eliminate answer choice C

E. 3x/y
If x = 1 and y = -1, then 3x/y = (3)(-1)/(1) = -3, which is not positive.
Eliminate answer choice E

By the process of elimination, the correct answer is D