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

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

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

simplify

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

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

Solution steps

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

Join

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

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

Apply the fraction rule:

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

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

Simplify

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

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

Apply the fraction rule:

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

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

Apply exponent rule:

aa = a^{2}

yy = y^{2}

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

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What is (1/y-y)(y+1/y) ?
The solution to (1/y-y)(y+1/y) is ((-y^2+1)(y^2+1))/(y^2)