Question

X/(x + 1) - 1/x = 1/(x ^ 2 + x)

Answer 1

Надеюсь все там понятно

Answer 2

Відповідь:

х = 2

Пояснення:

Answer 3

To solve the equation, let's simplify the expressions and find a common denominator:

X/(x + 1) - 1/x = 1/(x^2 + x)

First, we'll find the common denominator for the fractions on the left side. The common denominator will be (x + 1) * x:

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

Next, we'll simplify the left side by combining like terms in the numerator:

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

Now, we'll simplify the right side by factoring out an x:

(X * x - x - 1) / [(x + 1) * x] = 1/[x(x + 1)]

To eliminate the denominators, we'll multiply both sides of the equation by [(x + 1) * x]:

[(X * x - x - 1) * x] = 1

Expanding the left side:

X * x^2 - x^2 - x = 1

Rearranging the terms:

X * x^2 - x^2 - x - 1 = 0

Now, we have a quadratic equation. Let's solve it by factoring or using the quadratic formula:

(x - 1)(X * x + 1) = 0

Now, we can set each factor equal to zero and solve for x:

1. x - 1 = 0 x = 1

2. X * x + 1 = 0 X * x = -1 x = -1/X

Therefore, the solutions to the equation are x = 1 and x = -1/X.