$$\frac{P}{2}-\frac{1}{4}=\frac{p}{3}$$
$P=\frac{2p}{3}+\frac{1}{2}$
$$6P-3=4p$$
$$6P=4p+3$$
$$\frac{6P}{6}=\frac{4p+3}{6}$$
$$P=\frac{4p+3}{6}$$
$$P=\frac{2p}{3}+\frac{1}{2}$$
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$p=\frac{3P}{2}-\frac{3}{4}$
$$4p=6P-3$$
$$\frac{4p}{4}=\frac{6P-3}{4}$$
$$p=\frac{6P-3}{4}$$
$$p=\frac{3P}{2}-\frac{3}{4}$$
