What is (1-1/(4z))(1-1/(2z)) ?

The solution to (1-1/(4z))(1-1/(2z)) is ((4z-1)(2z-1))/(8z^2)

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simplify (1-1/(4z))(1-1/(2z))

simplify

(1 - \frac{1}{4 z}) (1 - \frac{1}{2 z})

\frac{( 4 z - 1 ) ( 2 z - 1 )}{8 z ^{2}}

Solution steps

(1 - \frac{1}{4 z}) (1 - \frac{1}{2 z})

Join

1 - \frac{1}{4 z} : \frac{4 z - 1}{4 z}

= \frac{4 z - 1}{4 z} (1 - \frac{1}{2 z})

Apply the fraction rule:

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

= \frac{( 4 z - 1 ) ( 1 - \frac{1}{2 z} )}{4 z}

Simplify

(4 z - 1) (1 - \frac{1}{2 z}) : \frac{( 4 z - 1 ) ( 2 z - 1 )}{2 z}

= \frac{\frac{( 4 z - 1 ) ( 2 z - 1 )}{2 z}}{4 z}

Apply the fraction rule:

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

= \frac{( 4 z - 1 ) ( 2 z - 1 )}{2 z \cdot 4 z}

Simplify

2 z \cdot 4 z : 8 z^{2}

= \frac{( 4 z - 1 ) ( 2 z - 1 )}{8 z ^{2}}

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What is (1-1/(4z))(1-1/(2z)) ?
The solution to (1-1/(4z))(1-1/(2z)) is ((4z-1)(2z-1))/(8z^2)