Question

X^2-4/x+x/x^2-4=3 1/3

Answer 1

Решение смотри на фото

Answer 2

To solve the equation $\frac{X^2-4}{x} + \frac{x}{x^2-4} = \frac{10}{3}$, we can follow these steps:

Step 1: Factor the denominators of the fractions: $x^2 - 4$ can be factored as $(x - 2)(x + 2)$.

Step 2: Write the fractions with the factored denominators: $\frac{x^2 - 4}{x} = \frac{(x - 2)(x + 2)}{x}$ and $\frac{x}{x^2 - 4} = \frac{x}{(x - 2)(x + 2)}$.

Step 3: Find a common denominator for the fractions on the left side of the equation: The common denominator for $\frac{(x - 2)(x + 2)}{x}$ and $\frac{x}{(x - 2)(x + 2)}$ is $(x - 2)(x + 2)$.

Step 4: Rewrite the fractions with the common denominator: $\frac{(x - 2)(x + 2)}{x} + \frac{x}{(x - 2)(x + 2)} = \frac{10}{3}$.

Step 5: Combine the fractions on the left side of the equation: $\frac{(x - 2)(x + 2) + x}{(x - 2)(x + 2)} = \frac{10}{3}$.

Step 6: Expand and simplify the numerator: $x^2 - 2x + 2x - 4 + x = \frac{10}{3}(x^2 - 4)$.

Simplify further: $x^2 - 4 = \frac{10}{3}(x^2 - 4)$.

Step 7: Distribute $\frac{10}{3}$ on the right side: $x^2 - 4 = \frac{10}{3}x^2 - \frac{40}{3}$.

Step 8: Move all terms to one side of the equation: $x^2 - \frac{10}{3}x^2 = - \frac{40}{3} + 4$.

Simplify: $-\frac{7}{3}x^2 = -\frac{28}{3}$.

Step 9: Divide both sides by $-\frac{7}{3}$ to solve for $x^2$: $x^2 = 4$.

Step 10: Take the square root of both sides to find $x$: $x = \pm 2$.

So, the solutions for the equation are $x = 2$ and $x = -2$.