$$\frac{5^{3}+5^{4}+5^{5}}{5^{2}+5^{3}+5^{4}}=?$$
$5$
$$\frac{125+5^{4}+5^{5}}{5^{2}+5^{3}+5^{4}}$$
$$\frac{125+625+5^{5}}{5^{2}+5^{3}+5^{4}}$$
$$\frac{750+5^{5}}{5^{2}+5^{3}+5^{4}}$$
$$\frac{750+3125}{5^{2}+5^{3}+5^{4}}$$
$$\frac{3875}{5^{2}+5^{3}+5^{4}}$$
$$\frac{3875}{25+5^{3}+5^{4}}$$
$$\frac{3875}{25+125+5^{4}}$$
$$\frac{3875}{150+5^{4}}$$
$$\frac{3875}{150+625}$$
$$\frac{3875}{775}$$
$$5$$
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