Question

Помогите решить уравнение с дробями: x^2/x^2+1=4-x^2/x^2+1 СРОЧНО!!!

Answer 1

(x-2)(x^2+2x+1)=4(x+1)(x-2)(x+1)^2 - 4(x+1) = 0.(x+1)( (x-2)(x+1) - 4 ) = 0.(x+1)( (x^2-x-6 ) = 0.Отсюда x= -1 или x^2-x-6=0.Решаем квадратное ур-е: x=(1-5)/2 = -2 или x=(1+5)/2 = 3.
Ответ: x = -1 или x = -2 или х = 3.

Answer 2

Solving the Equation with Fractions

To solve the equation x^2/(x^2 + 1) = 4 - x^2/(x^2 + 1), we can follow these steps:

Step 1: Multiply both sides of the equation by (x^2 + 1) to eliminate the denominators:

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

Simplifying, we get:

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

Step 2: Expand the right side of the equation:

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

Simplifying further, we have:

0 = 3x^2 + 4 - x^4

Step 3: Rearrange the equation to bring all terms to one side:

x^4 + 3x^2 - 4 = 0

Now, we have a quadratic equation in terms of x^2. We can solve this equation by factoring or using the