Question

3/x²-4x+4= 4/x²-4 +1/x+2​

Answer 1

Ответ:.

Пошаговое объяснение:

Answer 2

To solve the equation $\frac{3}{x^2 - 4x + 4} = \frac{4}{x^2 - 4} + \frac{1}{x+2}$, you can follow these steps:

1. Factor the denominators of the fractions on the right-hand side: $x^2 - 4x + 4 = (x - 2)^2$ $x^2 - 4 = (x - 2)(x + 2)$

2. Rewrite the equation with the factored denominators: $\frac{3}{(x - 2)^2} = \frac{4}{(x - 2)(x + 2)} + \frac{1}{x + 2}$

3. Find a common denominator for the fractions on the right-hand side, which is $(x - 2)^2(x + 2)$:

   $\frac{3}{(x - 2)^2} = \frac{4(x + 2)}{(x - 2)^2(x + 2)} + \frac{(x - 2)^2}{(x - 2)^2(x + 2)}$

4. Now that the denominators are the same, you can combine the fractions on the right-hand side:

   $\frac{3}{(x - 2)^2} = \frac{4(x + 2) + (x - 2)^2}{(x - 2)^2(x + 2)}$

5. Multiply both sides of the equation by the common denominator to clear the fractions:

   $3 = 4(x + 2) + (x - 2)^2$

6. Expand and simplify the equation:

   $3 = 4x + 8 + x^2 - 4x + 4$

   $3 = x^2 + 12$

7. Move the constant to the right side of the equation:

   $x^2 = -9$

8. Take the square root of both sides:

   $x = \pm 3i$

So, the solutions to the equation are $x = 3i$ and $x = -3i$. These are complex solutions because the equation involved complex numbers in the intermediate steps.