What is (z-1/y)(z+1/y) ?

The solution to (z-1/y)(z+1/y) is ((zy-1)(zy+1))/(y^2)

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simplify (z-1/y)(z+1/y)

simplify

(z - \frac{1}{y}) (z + \frac{1}{y})

\frac{( zy - 1 ) ( zy + 1 )}{y ^{2}}

Solution steps

(z - \frac{1}{y}) (z + \frac{1}{y})

Join

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

= \frac{zy - 1}{y} (z + \frac{1}{y})

Apply the fraction rule:

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

= \frac{( zy - 1 ) ( z + \frac{1}{y} )}{y}

Simplify

(zy - 1) (z + \frac{1}{y}) : \frac{( zy - 1 ) ( zy + 1 )}{y}

= \frac{\frac{( zy - 1 ) ( zy + 1 )}{y}}{y}

Apply the fraction rule:

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

= \frac{( zy - 1 ) ( zy + 1 )}{yy}

Apply exponent rule:

aa = a^{2}

yy = y^{2}

= \frac{( zy - 1 ) ( zy + 1 )}{y ^{2}}

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