Question

4x-6/x+2 - x/x+1 = 9/x^2+3x+2

Answer 1

Ответ:

Смотри решение на фото.

Answer 2

To solve the equation (4x - 6)/(x + 2) - x/(x + 1) = 9/(x^2 + 3x + 2), we can start by finding a common denominator for all the fractions on the left side of the equation. The common denominator will be (x + 2)(x + 1), which is also equal to (x^2 + 3x + 2).

Now, let's rewrite the equation with the common denominator:

(4x - 6)/(x + 2)(x + 1) - x/(x + 2)(x + 1) = 9/(x^2 + 3x + 2)

Now, we can combine the fractions on the left side:

[(4x - 6 - x)]/(x + 2)(x + 1) = 9/(x^2 + 3x + 2)

Simplify the numerator on the left side:

(3x - 6)/(x + 2)(x + 1) = 9/(x^2 + 3x + 2)

Next, we can cross-multiply to eliminate the fractions:

(3x - 6) * (x^2 + 3x + 2) = 9 * (x + 2)(x + 1)

Now, distribute on both sides:

3x(x^2 + 3x + 2) - 6(x^2 + 3x + 2) = 9(x^2 + 3x + 2)

Now, simplify further:

3x^3 + 9x^2 + 6x - 6x^2 - 18x - 12 = 9x^2 + 27x + 18

Combine like terms on both sides:

3x^3 + (9x^2 - 6x^2 - 9x^2) + (6x - 18x - 27x) - 12 - 18 = 0

Now, simplify further:

3x^3 - 12x^2 - 39x - 30 = 0

Now, let's factor out a common factor of 3:

3(x^3 - 4x^2 - 13x - 10) = 0

Now, we need to solve the cubic equation x^3 - 4x^2 - 13x - 10 = 0. Unfortunately, this cubic equation does not have a simple solution using elementary algebraic methods. You may need to use numerical methods or a calculator to find approximate solutions for x.

You can use numerical methods like the Newton-Raphson method or a graphing calculator to find approximate solutions for x.