Question

5/x²+2x+1=2/1-x²+1/x-1​

Answer 1

Ответ:

х=4

1)5/х2+2х=25/х+2/х=27/х+1=28/х.

2)2/1-х2=4/1х+1/х-1=24/х

3)28/х-24/х=4х

Х=4х=4

Думаю так можна Лудший ответ?

Answer 2

To solve the equation (5/x^2 + 2x + 1) = (2/(1 - x^2)) + (1/(x - 1)), we'll need to simplify and manipulate the expression to isolate the variable x. Let's proceed step by step:

Step 1: Simplify the expression on the right side: (2/(1 - x^2)) + (1/(x - 1))

To combine the two fractions, we need a common denominator. The common denominator here is (1 - x^2)(x - 1):

[2(x - 1) + (1 - x^2)] / [(1 - x^2)(x - 1)]

Simplifying the numerator: [2x - 2 + 1 - x^2] / [(1 - x^2)(x - 1)] [3x - 1 - x^2] / [(1 - x^2)(x - 1)]

Step 2: Replace the expression on the right side of the equation with the simplified form: 5/x^2 + 2x + 1 = [3x - 1 - x^2] / [(1 - x^2)(x - 1)]

Step 3: Clear the fractions by multiplying both sides of the equation by the common denominator [(1 - x^2)(x - 1)]: 5(x - 1)(1 - x^2) + x^2(x - 1) = 3x - 1 - x^2

Simplifying the left side of the equation: 5(x - 1 - x^2 + x^3 - x + x^3 - x^2) + x^3 - x^2 = 3x - 1 - x^2

Simplifying further: 5(-1 + x - x^2 + 2x^3) + x^3 - x^2 = 3x - 1 - x^2

Step 4: Expand and simplify the equation: -5 + 5x - 5x^2 + 10x^3 + x^3 - x^2 = 3x - 1 - x^2

Combining like terms: 10x^3 + x^3 - 5x^2 - x^2 - 3x + 5x - 3 = 0

11x^3 - 6x^2 + 2x - 3 = 0

At this point, we have obtained a cubic equation. To solve for x, you may use numerical methods such as numerical approximation or calculators that can solve cubic equations.