<s>[INST] Are these fractions all equal? Are the following expressions all equal to one another?
(2ab+c)/y

(2ab)/y + c/y

(2a)/y * (2b/y) + c/y

$$\dfrac{2ab+c}{y}=\dfrac{2ab}{y}+\dfrac{c}{y}=\dfrac{2a}{y}×\dfrac{2b}{y}+\dfrac{c}{y}$$
 [/INST] By starting with the first, and applying the distributive law, we get the second: $$\frac{2ab+c}{y} = (2ab+c) \frac{1}{y} = 2ab \frac{1}{y} + c \frac{1}{y} = \frac{2ab}{y} + \frac{c}{y}$$
The last one is not equal to the other two, because
$$\frac{2a}{y} \cdot \frac{2b}{y}  + \frac{c}{y}= \frac{2a\cdot 2b}{y\cdot y} + \frac{c}{y} = \frac{4ab}{y^2} + \frac{c}{y},$$
and $\frac{4ab}{y^2} + \frac{c}{y}$ is (usually) not equal to $\frac{2ab}{y} + \frac{c}{y}$. Notice that we used the fact that 
$$\frac{a}{b} \cdot \frac{c}{d} = \frac{ac}{bd}.$$
So the first two are equal, but not the third. 
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