Don't break up each property into a left and right side. Rather, accept the first property as true, then use it to prove the second--in your example, take the first equation and divide by x^2 to get the second one. Then start over, accepting only the second property as true, and use it to prove the first (in this case, by multiplying by x^2).

In other words, two propositions are equivalent if each implies the other.