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$$\dfrac{p}{p+3}=\dfrac{2p-1}{2p}$$

Get $p$. How can one solve these type of questions? What is the easiest and quickest method?

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    What's wrong with $2p^2=(2p-1)(p+3)$? Of course under the conditions $p \neq 0$ and $p+3 \neq 0$. From a geometrical point of view, you are looking for the intersection points of two hyperbolas, and it is natural that you should solve a second order equation.2012-10-06
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    You've gotten answers, but generally, you want to simplify in an efficient way that produces correct results. For ratio problems like this, the typical approach is cross multiply, simplify, gather like terms and then solve resulting problem.2012-10-06

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