5/x²+2x+1 - 2/1-x² = 1/x-1

To solve this equation, we can start by finding a common denominator for the fractions on both sides of the equation.

The common denominator for x²+2x+1 is (x+1)(x+1), and the common denominator for 1-x² is (1-x)(1+x).

Multiplying the entire equation by the common denominators, we get:

[(5(x+1)(x+1))/(x+1)(x+1)] - [(2(1+x))/(1-x)(1+x)] = [(1)/(x-1)] * [(1+x)(1-x)]

Simplifying the equation, we have:

5(x+1) - 2(1+x) = 1

Expanding the brackets:

5x + 5 - 2 - 2x = 1

Combine like terms:

3x + 3 = 1

Subtracting 3 from both sides:

3x = -2

Dividing both sides by 3:

x = -2/3

Therefore, the value of x that satisfies the equation is -2/3.