Question

((a-1/a)^2-a)-((a-1/a)+a)^2=

Answer 1

Ответ:

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Answer 2

To simplify the expression ((a-1/a)^2-a)-((a-1/a)+a)^2, let's break it down step by step:

Step 1: Simplify the square of (a-1/a): (a-1/a)^2 = (a^2 - 2 + 1/a^2) = (a^2 + 1/a^2 - 2)

Step 2: Simplify (a-1/a) + a: (a-1/a) + a = a - 1/a + a = 2a - 1/a

Step 3: Simplify the square of (a-1/a) + a: ((a-1/a) + a)^2 = (2a - 1/a)^2 = (4a^2 - 4 + 1/a^2)

Now let's substitute these results back into the original expression:

((a-1/a)^2-a)-((a-1/a)+a)^2 = (a^2 + 1/a^2 - 2) - (4a^2 - 4 + 1/a^2) = a^2 + 1/a^2 - 2 - 4a^2 + 4 - 1/a^2 = -3a^2 + 2 + 2/a^2

Therefore, the simplified expression is -3a^2 + 2 + 2/a^2.