a³ - 1/a³ - 2a + 2/a
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A³-1/a³-2a+2/a
=( a)³ - (1/a) ³-2a+2/a
= (a) ³- (1/a) ³-2{a-(1/a)}
now, we got a number in the form of a^3 - b^3 which equal (a-b)( a² + ab +b²)
= {a -(1/a)} { a² + (a)(1/a) + (1/a²)} - 2 {a -(1/a)}
= {a -(1/a)} ( a² + 1 + (1/a²) -2)
= {a -(1/a)} {a²-1 (1/a²)}
=( a)³ - (1/a) ³-2a+2/a
= (a) ³- (1/a) ³-2{a-(1/a)}
now, we got a number in the form of a^3 - b^3 which equal (a-b)( a² + ab +b²)
= {a -(1/a)} { a² + (a)(1/a) + (1/a²)} - 2 {a -(1/a)}
= {a -(1/a)} ( a² + 1 + (1/a²) -2)
= {a -(1/a)} {a²-1 (1/a²)}
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