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If p ≠ 0 and p – (1 – p^2 )/p = r/p, then r =

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If p ≠ 0 and p – (1 – p^2 )/p = r/p, then r = [#permalink]

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If p ≠ 0 and \(p – \frac{(1 – p^2 )}{p} =\frac{r}{p}\), then r =


A) p + 1

B) 2p – 1

C) \(p^2+ 1\)

D) \(2p^2 – 1\)

E) \(p^2 + p – 1\)


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Last edited by AbdurRakib on 22 Jun 2016, 13:19, edited 1 time in total.

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Re: If p ≠ 0 and p – (1 – p^2 )/p = r/p, then r = [#permalink]

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AbdurRakib wrote:
If p ≠ 0 and p – {\(\frac{(1 – p2 )}{p}\)} = \(\frac{r}{p}\), then r =

A) p + 1
B) 2p – 1
C) \(p^2\)+ 1
D) 2\(p^2\) – 1
E) \(p^2\) + p – 1

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\(p –\frac{(1 – p^2 )}{p} = \frac{p^2 –(1 – p^2 )}{p} = \frac{p^2 –1 + p^2}{p} = \frac{2p^2 –1}{p} = \frac{r}{p}\).................
\(r= 2p^2-1\)

D
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Re: If p ≠ 0 and p – (1 – p^2 )/p = r/p, then r = [#permalink]

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New post 22 Jun 2016, 13:12
AbdurRakib equation is missing an indication of power for "p2".

I actually thought it was a typo for 2p. :(

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Re: If p ≠ 0 and p – (1 – p^2 )/p = r/p, then r = [#permalink]

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New post 22 Jun 2016, 13:20
arthurmatsuda wrote:
AbdurRakib equation is missing an indication of power for "p2".

I actually thought it was a typo for 2p. :(


edited

thanks for your remarks
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Re: If p ≠ 0 and p – (1 – p^2 )/p = r/p, then r = [#permalink]

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AbdurRakib wrote:
If p ≠ 0 and p – {\(\frac{(1 – p^2 )}{p}\)} = \(\frac{r}{p}\), then r =

A) p + 1
B) 2p – 1
C) \(p^2\)+ 1
D) 2\(p^2\) – 1
E) \(p^2\) + p – 1


We are given that p - [(1-p^2)/p] = r/p, and we must isolate r.

We can start by multiplying the entire equation by p and then simplifying:

p^2 - (1 - p^2) = r

p^2 - 1 + p^2 = r

2p^2 - 1 = r

Answer: D
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Re: If p ≠ 0 and p – (1 – p^2 )/p = r/p, then r = [#permalink]

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New post 19 Feb 2017, 10:28
Isolating r,
we get
r = p [ p - {(1-p^2)/p} ]

r= p^2 - (1-p^2)

r= p^2 - 1 + p^2

r= 2p^2 - 1 = answer is D.

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Re: If p ≠ 0 and p – (1 – p^2 )/p = r/p, then r = [#permalink]

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New post 04 Apr 2017, 22:31
\(p-\cfrac { \left( 1-{ p }^{ 2 } \right) }{ p } =\cfrac { r }{ p } \\ \left[ p\left( p-\cfrac { \left( 1-{ p }^{ 2 } \right) }{ p } =\cfrac { r }{ p } \right) \right] \\ { p }^{ 2 }-\left( 1-{ p }^{ 2 } \right) =r\\ { p }^{ 2 }-1+{ p }^{ 2 }=r\\ 2{ p }^{ 2 }-1=r\)

PEMDAS in the 3rd line got me thinking whether I should multiply that negative to \(\left( 1-{ p }^{ 2 } \right)\).
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Re: If p ≠ 0 and p – (1 – p^2 )/p = r/p, then r = [#permalink]

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New post 26 Jul 2017, 03:23
Bunuel

How to know if 1-p^2 is in bracket or not?

I found r=-1 because of this error.
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Re: If p ≠ 0 and p – (1 – p^2 )/p = r/p, then r = [#permalink]

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Re: If p ≠ 0 and p – (1 – p^2 )/p = r/p, then r = [#permalink]

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New post 17 Sep 2017, 23:46
Bunuel. Once we multiply both sides by p, p in the numerator becomes p^2, but what happens to the p in the denumerator? I understand that it gets cancel, but I don't see how.

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Re: If p ≠ 0 and p – (1 – p^2 )/p = r/p, then r = [#permalink]

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Valentina86 wrote:
If p ≠ 0 and \(p – \frac{(1 – p^2 )}{p} =\frac{r}{p}\), then r =


A) p + 1

B) 2p – 1

C) \(p^2+ 1\)

D) \(2p^2 – 1\)

E) \(p^2 + p – 1\)

Bunuel. Once we multiply both sides by p, p in the numerator becomes p^2, but what happens to the p in the denumerator? I understand that it gets cancel, but I don't see how.


\(p – \frac{(1 – p^2 )}{p} =\frac{r}{p}\);

Multiply by p: \(p*(p – \frac{(1 – p^2 )}{p}) =p*\frac{r}{p}\);

Expand the left hand side and reduce by p in the right hand side: \(p^2 – p*\frac{(1 – p^2 )}{p} =r\);

Reduce by p in the second term on the left hand side: \(p^2 –(1 – p^2 ) =r\);

Open the brackets: \(p^2 –1 + p^2 =r\);

\(2p^2-1=r\)

Answer: D.

Hope it's clear.
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Re: If p ≠ 0 and p – (1 – p^2 )/p = r/p, then r =   [#permalink] 17 Sep 2017, 23:52
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