So sánh
\(A = \frac{{{{10}^8} + 2}}{{{{10}^8} - 1}};B = \frac{{{{10}^8}}}{{{{10}^8} - 3}}\)
\(\begin{array}{l}
A = \frac{{{{10}^8} + 2}}{{{{10}^8} - 1}} = \frac{{{{10}^8} - 1 + 3}}{{{{10}^8} - 1}}\\
= \frac{{{{10}^8} - 1}}{{{{10}^8} - 1}} + \frac{3}{{{{10}^8} - 1}}\\
= 1\frac{3}{{{{10}^8} - 1}}\\
B = \frac{{{{10}^8}}}{{{{10}^8} - 3}} = \frac{{{{10}^8} - 3 + 3}}{{{{10}^8} - 3}}\\
= \frac{{{{10}^8} - 3}}{{{{10}^8} - 3}} + \frac{3}{{{{10}^8} - 3}}\\
= 1\frac{3}{{{{10}^8} - 3}}
\end{array}\)
Vì \(1\frac{3}{{{{10}^8} - 1}} < 1\frac{3}{{{{10}^8} - 3}}\) nên A < B
-- Mod Toán 6
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