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Algebra Difficulty 1.8 Junior Find the answer

The value of 24−223−1\frac{2^4 - 2}{2^3 - 1} is?

A number or a short expression. Spacing and $ signs are ignored.

Solution

We note that 23=2×2×2=82^3 = 2 \times 2 \times 2 = 8 and 24=23×2=162^4 = 2^3 \times 2 = 16. Therefore, 24−223−1=16−28−1=147=2\frac{2^4 - 2}{2^3 - 1} = \frac{16 - 2}{8 - 1} = \frac{14}{7} = 2. Alternatively, 24−223−1=2(23−1)23−1=2\frac{2^4 - 2}{2^3 - 1} = \frac{2(2^3 - 1)}{2^3 - 1} = 2.

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