I think I misunderstood a part of a book

we can't multiply or divide both sides of an equation by 0 right?

in one part of that book.

we have this rational equation

\(\displaystyle \frac{2x}{(x-3)} + \frac{5}{(x+3)} = \frac{36}{(x^2-9)}\)

for solving it we multiply both side by lcd that is\(\displaystyle (x-3)(x+3)\)

and solve the equation \(\displaystyle 2x(x+3) + 5(x-3) = 36\) the answers will be \(\displaystyle x=\frac{-17}{2}\) and \(\displaystyle x = 3\)

so if \(\displaystyle x = 3\) that means \(\displaystyle (x-3) = 0 \) and we are multiplying both sides by 0

can we do that ? or I'm missing something or totally misunderstood the subject

thank you.