Решите уравнение

(1+х) (2+х) / х^2-х-2

Выражение: (1+x) * (2+x) / x^2-x-2

Ответ: 2/x^2+3/x-1-x

Решаем по действиям:

1. (1+x) * (2+x) = 2+3*x+x^2

(1+x) * (2+x) = 1*2+1*x+x*2+x*x

1.1. x+x*2=3*x

1.2. x*x=x^2

x*x=x^ (1+1)

1.2.1. 1+1=2

+1

_1_

2

2. (2+3*x+x^2) / x^2=2/x^2+3*x/x^2+x^2/x^2

3. x/x^2=x^ (-1)

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

3.1. 1-2=-1

-2

_1_

-1

4. x^ (-1) = 1/x

5. x^2/x^2=1

6. 1-2=-1

-2

_1_

-1

Решаем по шагам:

1. (2+3*x+x^2) / x^2-x-2

1.1. (1+x) * (2+x) = 2+3*x+x^2

(1+x) * (2+x) = 1*2+1*x+x*2+x*x

1.1.1. x+x*2=3*x

1.1.2. x*x=x^2

x*x=x^ (1+1)

1.1.2.1. 1+1=2

+1

_1_

2

2. 2/x^2+3*x/x^2+x^2/x^2-x-2

2.1. (2+3*x+x^2) / x^2=2/x^2+3*x/x^2+x^2/x^2

3. 2/x^2+3*x^ (-1) + x^2/x^2-x-2

3.1. x/x^2=x^ (-1)

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

3.1.1. 1-2=-1

-2

_1_

-1

4. 2/x^2+3/x+x^2/x^2-x-2

4.1. x^ (-1) = 1/x

5. 2/x^2+3/x+1-x-2

5.1. x^2/x^2=1

6. 2/x^2+3/x-1-x

6.1. 1-2=-1

-2

_1_

-1