Question

Розв'язати рівняння: 4/ x^2+2x+1 - 1/x^2-2x+1 = - 1/x^2 - 1

Answer 1

To simplify the given expression, let's first find a common denominator for the fractions:

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

The common denominator is (x^2 + 2x + 1)(x^2 - 2x + 1)(x^2 - 1). Multiplying each term by the common denominator:

4(x^2 - 1) - (x^2 + 2x + 1) - (x^2 - 2x + 1) = -1

Expanding and simplifying:

4x^2 - 4 - x^2 - 2x - 1 - x^2 + 2x - 1 = -1

Combining like terms:

2x^2 - 4 = 0

Dividing both sides by 2:

x^2 - 2 = 0

Now we have the equation x^2 - 2 = 0.