How is $P=4P−3RP$ equal to $1=4−3R$

Question

How is $P=4P−3RP$ equal to $1=4−3R$ when by dividing both sides by $P$ one eliminates two $P's$ at the right side of the equation while having only one $P$ in the denominator.

Answer 1

Dividing both sides of the equation by $P\require{cancel}$, under the provision $P\neq 0$: $$\frac PP = \frac{ 4P - 3RP}P \iff 1\overset{\color{red}{\Large *}}= \frac{(4-3R)P}P = \frac{(4-3R)\cancel{P}}{\cancel{P}} = {4-3R}$$

$\color{red} {\large *}$ This equivalence follows from the distributive property of multiplication over addition.

Answer 2

By the distributive property of multiplication with respect to addition (see http://en.wikipedia.org/wiki/Distributive_property) one has

$$ 4P−3RP = (4-3R)P $$

so now it's evident that you can divide both sides of

$$ P=(4-3R)P $$

by $P$ and obtain the solution.