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# If r > 0, s ≠ 1/2 and r = 3s +1/1-2s, then s=

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If r > 0, s ≠ 1/2 and r = 3s +1/1-2s, then s= [#permalink]  15 Jun 2017, 08:07
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0% (00:00) correct 0% (00:00) wrong based on 0 sessions

If r > 0, s ≠ \frac{1}{2} and r = \frac{3s +1}{1-2s}, then s=

A) \frac{3r}{12 +6r}

B) \frac{-2r}{3}

C) \frac{r-1}{3+2r}

D) \frac{2}{3(1-r)}

E) \frac{-1+r}{3}
[Reveal] Spoiler: OA

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Re: If r > 0, s ≠ 1/2 and r = 3s +1/1-2s, then s= [#permalink]  15 Jun 2017, 13:41
Expert's post
Carcass wrote:

If r > 0, s ≠ \frac{1}{2} and r = \frac{3s +1}{1-2s}, then s=

A) \frac{3r}{12 +6r}

B) \frac{-2r}{3}

C) \frac{r-1}{3+2r}

D) \frac{2}{3(1-r)}

E) \frac{-1+r}{3}

Given: r = \frac{3s +1}{1-2s}

Multiply both sides by (1 - 2s) to get: r(1 - 2s) = 3s + 1
Expand: r - 2rs = 3s + 1
NOTE: We want the s's on one side. So....
Add 2rs to both sides: r = 3s + 2rs + 1
Subtract 1 from both sides: r - 1 = 3s + 2rs
Factor right side: r - 1 = s(3 + 2r)
Divide both sides by (3 + 2r) to get: (r - 1)/(3 + 2r) = s

[Reveal] Spoiler:
C

Cheers,
Brent
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Re: If r > 0, s ≠ 1/2 and r = 3s +1/1-2s, then s=   [#permalink] 15 Jun 2017, 13:41
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