Question

18-x^2- 3x/x^2 +6x =1+ 3/x+2

Answer 1

Ответ: приложено

Объяснение:

Answer 2

To solve the equation, let's simplify it step by step:

1. Start by multiplying both sides of the equation by the denominator of the fractions to eliminate them:

   (18 - x^2 - 3x)(x^2 + 6x) = (x + 2)(x^2 + 6x) + 3(x^2 + 6x)

   Simplifying the left side:

   (18 - x^2 - 3x)(x^2 + 6x) = 18x^2 + 108x - x^4 - 6x^3 - 3x^3 - 18x^2

   Simplifying the right side:

   (x + 2)(x^2 + 6x) + 3(x^2 + 6x) = x^3 + 2x^2 + 6x^2 + 12x + 3x^2 + 18x

   Combining like terms:

   18x^2 + 108x - x^4 - 6x^3 - 3x^3 - 18x^2 = x^3 + 2x^2 + 6x^2 + 12x + 3x^2 + 18x

2. Next, simplify the equation by arranging the terms in descending order of exponents:

   -x^4 - 6x^3 - 3x^3 + x^3 + 18x^2 + 18x^2 + 6x^2 + 3x^2 + 108x + 12x + 18x = 0

   Combining like terms:

   -x^4 - 8x^3 + 27x^2 + 138x = 0

3. Now, let's rearrange the equation to isolate the terms with x:

   -x^4 - 8x^3 + 27x^2 + 138x = 0

   x(-x^3 - 8x^2 + 27x + 138) = 0

4. Since the product of two factors is equal to zero, we can set each factor equal to zero and solve for x:

   x = 0

   -x^3 - 8x^2 + 27x + 138 = 0

At this point, solving the cubic equation for x will require more advanced techniques such as factoring, synthetic division, or using numerical methods like Newton's method. Unfortunately, the equation is quite complicated, and I won't be able to provide an exact solution here. You may need to use a graphing calculator or computer software to find the approximate values of x that satisfy the equation.