If we have 2 fractions and set them equal to each other, can we remove the numerator without changing the equation? So the demonators would just equal eachother, so $4p = 8$ Like this:
$$\frac{1}{4p} = \frac{1}{8}$$
Multiply each side by 4p:
$$\frac{4p*1}{4p} = \frac{4p*1}{8}$$
Then we cross out each 4p on the LHS:
$$1 = \frac{4p}{8}$$
Then times each side by 8 to isolate p:
$$1*8 = \frac{4p*8}{8}$$
And finnally we cross out each 8 on the LHS and left with:
$$8= 4p$$
Can we do this with any number? Assuming of course the number is real.
Best Answer
Suppose we have $$\frac{a}{b}=\frac{a}{c}$$
where $a \ne 0$.
Multiplying both sides by $\frac{bc}{a}$ gives us $c=b$.