What is (1-1/z)(1-(0.2)/z) ?

The solution to (1-1/z)(1-(0.2)/z) is ((z-1)(5z-1))/(5z^2)

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simplify (1-1/z)(1-(0.2)/z)

simplify

(1 - \frac{1}{z}) (1 - \frac{0.2}{z})

\frac{( z - 1 ) ( 5 z - 1 )}{5 z ^{2}}

Solution steps

(1 - \frac{1}{z}) (1 - \frac{0.2}{z})

Join

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

= \frac{z - 1}{z} (1 - \frac{0.2}{z})

Simplify

1 - \frac{0.2}{z} : 1 - \frac{1}{5 z}

= \frac{z - 1}{z} (1 - \frac{1}{5 z})

Apply the fraction rule:

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

= \frac{( z - 1 ) ( 1 - \frac{1}{5 z} )}{z}

Simplify

(z - 1) (1 - \frac{1}{5 z}) : \frac{( z - 1 ) ( 5 z - 1 )}{5 z}

= \frac{\frac{( z - 1 ) ( 5 z - 1 )}{5 z}}{z}

Apply the fraction rule:

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

= \frac{( z - 1 ) ( 5 z - 1 )}{5 zz}

Apply exponent rule:

aa = a^{2}

zz = z^{2}

= \frac{( z - 1 ) ( 5 z - 1 )}{5 z ^{2}}

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What is (1-1/z)(1-(0.2)/z) ?
The solution to (1-1/z)(1-(0.2)/z) is ((z-1)(5z-1))/(5z^2)