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Which of the following does the expression 3^b + 3^b-1/3^b+1-3^b

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Joined: 26 Apr 2018
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Which of the following does the expression 3^b + 3^b-1/3^b+1-3^b  [#permalink]

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Updated on: 23 Sep 2018, 03:13
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Which of the following does the expression $$\frac{3^b + 3^{b-1}}{3^{b+1}-3^b}$$ equal.

a) 3
b) 4/3
c) 3/2
d) 3/4
e) 2/3

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Originally posted by bettatantalo on 22 Sep 2018, 07:11.
Last edited by Bunuel on 23 Sep 2018, 03:13, edited 1 time in total.
Edited the question.
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Joined: 12 Sep 2015
Posts: 4226
Re: Which of the following does the expression 3^b + 3^b-1/3^b+1-3^b  [#permalink]

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22 Sep 2018, 09:31
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bettatantalo wrote:
Which of the following does the expression 3$$^{b}$$ + 3$$^{b-1}$$/3$$^{b+1}$$-3$$^{b}$$ equal.

a) 3
b) 4/3
c) 3/2
d) 3/4
e) 2/3

One approach is to assign a nice/easy value to b and evaluate the expression.

We get: (3^1 + 3^0)/(3^2 - 3^1)
Evaluate each power to get: (3 + 1)/(9 - 3)
Evaluate again: 4/6
Simplify: 1/3

Cheers,
Brent
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Which of the following does the expression 3^b + 3^b-1/3^b+1-3^b  [#permalink]

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22 Sep 2018, 17:39
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bettatantalo wrote:
Which of the following does the expression 3$$^{b}$$ + 3$$^{b-1}$$/3$$^{b+1}$$-3$$^{b}$$ equal.

a) 3
b) 4/3
c) 3/2
d) 3/4
e) 2/3

Sorry for the non existent fraction formatting but it kept turning out weird.

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GMATPrepNow , I think you meant $$\frac{2}{3}$$.

The approach above is my preference.

Algebraically:
$$\frac{3^{b}+3^{b-1}}{3^{b+1}-3^{b}}=$$

$$\frac{3^{b}(1+3^{-1})}{3^{b}(3^1-1)}=$$

$$\frac{1+3^{-1}}{2}=\frac{1+\frac{1}{3}}{2}=$$

$$\frac{(\frac{4}{3})}{2}=(\frac{4}{3}*\frac{1}{2})=\frac{4}{6}=\frac{2}{3}$$

bettatantalo , the other day a boorish poster treated you rudely. I commend you for trying to format properly. Try this trick: for formats you want to learn, "peek" at the formatting. Let's say you want to learn how to write compound fractions as I have in the final "math" line of this post. 1) get a picture of the "polished" format by screenshotting my post; then 2) get a peek at the formatting. Hit "reply" on my post. You will see the coded formatting. Take another screenshot. Then choose "cancel" or close the tab (your fake reply will not post). And ignore incivilty.
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Which of the following does the expression 3^b + 3^b-1/3^b+1-3^b   [#permalink] 22 Sep 2018, 17:39
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