化简 (2-1/(2^n))(3+1/(2^n))

解答

化简

(2 - \frac{1}{2 ^{n}}) (3 + \frac{1}{2 ^{n}})

\frac{( 2 ^{1 + n} - 1 ) ( 3 \cdot 2 ^{n} + 1 )}{4 ^{n}}

求解步骤

(2 - \frac{1}{2 ^{n}}) (3 + \frac{1}{2 ^{n}})

合并

2 - \frac{1}{2 ^{n}} : \frac{2 ^{1 + n} - 1}{2 ^{n}}

= \frac{2 ^{1 + n} - 1}{2 ^{n}} (3 + \frac{1}{2 ^{n}})

使用分式法则:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{( 2 ^{1 + n} - 1 ) ( 3 + \frac{1}{2 ^{n}} )}{2 ^{n}}

化简

(2^{1 + n} - 1) (3 + \frac{1}{2 ^{n}}) : \frac{( 2 ^{1 + n} - 1 ) ( 3 \cdot 2 ^{n} + 1 )}{2 ^{n}}

= \frac{\frac{( 2 ^{1 + n} - 1 ) ( 3 \cdot 2 ^{n} + 1 )}{2 ^{n}}}{2 ^{n}}

使用分式法则:

\frac{\frac{a}{b}}{c} = \frac{a}{b \cdot c}

= \frac{( 2 ^{1 + n} - 1 ) ( 3 \cdot 2 ^{n} + 1 )}{2 ^{n} \cdot 2 ^{n}}

化简

2^{n} \cdot 2^{n} : 4^{n}

= \frac{( 2 ^{1 + n} - 1 ) ( 3 \cdot 2 ^{n} + 1 )}{4 ^{n}}

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