$$12\div(1+2)\ne(12\div1)+(12\div2^{2}$$
$\text{true}$
$$\frac{12}{3}\neq \frac{12}{1}+\frac{12}{2^{2}}$$
$$4\neq \frac{12}{1}+\frac{12}{2^{2}}$$
$$4\neq 12+\frac{12}{2^{2}}$$
$$4\neq 12+\frac{12}{4}$$
$$4\neq 12+3$$
$$4\neq 15$$
$$\text{true}$$
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