I'm having some problems to understand a simplification and I know the correct answer but I'd like to understand why my method is wrong or what rule I'm breaking.
I have an equation like the following:
$$Fr \cdot \left( \frac1{Sr} + \frac1{Sp} \right) = \frac{Ft}{Sp}$$
Where the variable I'm looking for is $Fr$. My tendency was to do:
$$ Fr = \frac{Ft}{Sp} \cdot ( Sr + Sp ) $$
But it seems to be wrong, I should have do:
$$ Ft \cdot \left( \frac{Sp + Sr}{Sr \cdot Sp} \right) = \frac{Ft}{Sp} $$
and then:
$$ Ft = \frac{Sr \cdot Sp \cdot Ft}{Sp + Sr} $$
Why I can not simply pass & inverse the fraction to the other side? Thanks so much!!
Because
$$ \frac1a + \frac1b \neq \frac1{a+b} $$
This is already the case for $a=b=1$, where one the left side you get $2$ and on the right side you get $\frac12$.