T2 Sec 3 #15

If you ask me, this one is begging for plug in. Say that x = 2. Then \dfrac{5x-2}{x+3} becomes \dfrac{5(2)-2}{2+3}=\dfrac{8}{5}. Which answer choice also equals \dfrac{8}{5} when x = 2?

A) \dfrac{5-2}{3}=1

B) 5-\dfrac{2}{3}=\dfrac{15}{3}-\dfrac{2}{3}=\dfrac{13}{3}

C) 5-\dfrac{2}{x+3}=5-\dfrac{2}{2+3}=5-\dfrac{2}{5}=\dfrac{25}{5}-\dfrac{2}{5}=\dfrac{23}{5}

D) 5-\dfrac{17}{x+3}=5-\dfrac{17}{2+3}=5-\dfrac{17}{5}=\dfrac{25}{5}-\dfrac{17}{5}=\dfrac{8}{5}

Only choice D equaled \dfrac{8}{5}, so D is the answer!

The mathy way, because I know someone’s going to want to see it, is to do polynomial division:


That’s 5 with a remainder of –17, which can also be written as 5-\dfrac{17}{x+3}.

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