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

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

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simplify (a-1/a)(a+1/a)

simplify

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

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

Solution steps

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

Join

a - \frac{1}{a} : \frac{a ^{2} - 1}{a}

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

Apply the fraction rule:

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

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

Simplify

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

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

Apply the fraction rule:

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

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

Apply exponent rule:

aa = a^{2}

aa = a^{2}

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

- 2 (3 - 5)

(5^{3})^{6}

3 (10 - 5)

\frac{11 x - 8}{x ( x - 4 )}

(2 + 2 a) \cdot (2 - 2 a)

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