So given: $\frac{2}{15x^2} + \frac{3}{5x}$ LCD: $15x^2$ Therefore you change the second term to a equal term with the LCD as its denominator by multiplying by $3x$: $\frac2{15x^2} + \frac{9x}{15x^2}$
For an answer of $\frac{2 + 9x}{15x^2}$ (correct)
My question is why can you not multiply the whole expression to begin with by the LCD? Why is the following not allowed:
$15x^2 (\frac{2}{15x^2} + \frac{3}{5x}) = 2 + 9x $(incorrect)
I know you can multiply the whole expression by LCD in complex rational expressions like:
$$\frac{2(1/2+1/2)}{2(1/2+1/2)}=\frac{1+1}{1+1}=\frac{2}{2}=1$$
( Assume you do not know a/a=1 ; I know its an easy example but Im using this just to show how it works in another scenario and ask why it works in one and not the first)
Thanks for helping me out with an easy problem, that I should really know by now...