<s>[INST] need help on this fraction equation $2/5 = 2/3 - r/5$ $$\frac{2}{5} = \frac{2}{3} - \frac{r}{5}$$
I'm trying to find $r$. Can anyone give me a step by step?
 [/INST] First note that
$$ \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm b}{c}$$
And
$$ \frac{a}{b}\pm c=\frac{a\pm bc}{c} $$
So now we have
$$\frac{2}{5} = \frac{2}{3} - \frac{r}{5} $$
$$\frac{2}{5} + \frac{r}{5} = \frac{2}{3} $$
$$\frac{2+r}{5} = \frac{2}{3} $$
$$ 2+r = \frac{2\times 5}{3} $$
$$ r = \frac{10}{3}-2 =\frac{10-(2\times 3)}{3}$$
$$r=\frac{10-6}{3}=\frac43$$
</s>