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Re: If p ≠ 0 and p – (1 – p^2 )/p = r/p, then r = [#permalink]
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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.
Re: If p ≠ 0 and p – (1 – p^2 )/p = r/p, then r = [#permalink]
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17 Sep 2017, 23:52
1
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: \(p^2 –(1 – p^2 ) =r\);
If you multiply or divide both the sides of a fraction by a variable/constant, the value remains the same
Another way to do this is as follows \(\frac{2p^2 –1}{p} = \frac{r}{p}\) -> \(2p^2 –1= \frac{r}{p}*p\) (by cross multiplying) -> r = 2\(p^2\) - 1
Here p on the right-hand side cancel each other out(because in a fraction, common number/variables in the numerator and denominator cancel each other out)
Hope this helps you!
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If p ≠ 0 and p – (1 – p^2 )/p = r/p, then r =
[#permalink]
01 Mar 2018, 12:53
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86% (00:49) correct 
