The expression (5x - 2)/(x + 3) is equivalent to which of the following?

[math_celebrity]

The expression (5x - 2)/(x + 3) is equivalent to which of the following?

• A) (5 - 2)/3
• B) 5 - 2/3
• C) 5 - (2/(x + 3))
• D) 5 - (17/(x + 3))

Let's start with an integer x = 2. Plug that into our original expression, and we get:
(5(2) - 2)(2 + 3)
(10 - 2)/5
8/5

So what we do next is, take x = 2, and plug it into answer choices A-D, and see which one results in 8/5
A) 3/3 = 1 <-- Nope
B) Since 5 is 15/3, we have 15/3 - 2/3 = 13/3 which is over 4, so Nope
C) 5 - (2/(2 + 3)) = 5 - (2/5). Since 5 is 25/5, we have 25/5 - 2/5 = 23/5. <-- Nope
D) 5 - (17/(2 + 3)) = 5 - 17/5. Since 5 is 25/5, we have 25/5 - 17/5 = 8/5 <-- YES

Since 8/5 = 8/5, our answer is D) 5 - (17/(x + 3))