Question

(x+1/x-1-x-1/x+1) : x/x^2-1

Answer 1

Ответ: = - 1

Объяснение: (x+1/x-1-x-1/x+1) : x/x^2-1 = (0+0+0) : x/x^2-1 = 0 : x/x^2-1 = 0-1 = - 1

Answer 2

Let's simplify the given expression step by step:

Expression: (x + 1) / (x - 1) - (x - 1) / (x + 1) : x / (x^2 - 1)

Step 1: Simplify the fractions in the numerator: (x + 1) / (x - 1) = (x + 1) / (x - 1) * (x + 1) / (x + 1) = (x^2 + 2x + 1) / (x^2 - 1)

(x - 1) / (x + 1) = (x - 1) / (x + 1) * (x - 1) / (x - 1) = (x^2 - 2x + 1) / (x^2 - 1)

Step 2: Combine the fractions in the numerator: [(x^2 + 2x + 1) - (x^2 - 2x + 1)] / (x^2 - 1) = (x^2 + 2x + 1 - x^2 + 2x - 1) / (x^2 - 1) = (4x) / (x^2 - 1) = 4x / [(x - 1)(x + 1)]

Step 3: Simplify the denominator: x / (x^2 - 1) = x / [(x - 1)(x + 1)]

Step 4: Divide the two fractions: (4x / [(x - 1)(x + 1)]) / (x / [(x - 1)(x + 1)]) = (4x / [(x - 1)(x + 1)]) * ([(x - 1)(x + 1)] / x) = 4

So, the simplified expression is 4.