Question

Help! (1+а^-2/1-а^-2)^-1

Answer 1

Выражение можно прочитать по-разному:
$1) (1 + \frac{a^{-2}}{1} - a^{-2} )^{-1} = ( 1 +a^{-2} - a^{-2} )^{-1} = 1^{-1} = \frac{1}{1^1} = \frac{1}{1} = 1 \\ \\ \\ 2)( \frac{1 + a^{-2}}{1 - a^{-2}} )^{-1}= \frac{1 -a^{-2}}{1+a^{-2}} = \frac{1 - \frac{1}{a^2} }{1+ \frac{1}{a^2} } = \frac{1*a^2 - 1}{a^2} : \frac{1*a^2 + 1}{a^2} = \frac{a^2-1}{a^2} * \frac{a^2}{a^2+1} = \frac{a^2-1}{a^2+1}$

Answer 2

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

Answer 3

To simplify the expression (1 + a^(-2) / (1 - a^(-2))^(-1), you can follow these steps:

1. First, flip the denominator, (1 - a^(-2)), so it becomes (1 - a^(-2))^(-1).

2. Now the expression is:

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

3. To simplify further, multiply the numerator and denominator by (1 - a^(-2)):

   [(1 + a^(-2)) * (1 - a^(-2))] / 1

4. Use the difference of squares identity, (a^2 - b^2) = (a + b)(a - b), to simplify the numerator:

   [(1 - a^4)] / 1

5. The final simplified expression is:

   1 - a^4

So, (1 + a^(-2) / (1 - a^(-2))^(-1) simplifies to 1 - a^4.