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

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Solution for 1/(x^2+3x+2)=(1/(x-2))+(2/(x^2-4)) equation: 


D( x )

x-2 = 0

x^2+3*x+2 = 0

x^2-4 = 0

x-2 = 0

x-2 = 0

x-2 = 0 // + 2

x = 2

x^2+3*x+2 = 0

x^2+3*x+2 = 0

x^2+3*x+2 = 0

DELTA = 3^2-(1*2*4)

DELTA = 1

DELTA > 0

x = (1^(1/2)-3)/(1*2) or x = (-1^(1/2)-3)/(1*2)

x = -1 or x = -2

x^2-4 = 0

x^2-4 = 0

1*x^2 = 4 // : 1

x^2 = 4

x^2 = 4 // ^ 1/2

abs(x) = 2

x = 2 or x = -2

x in (-oo:-2) U (-2:-1) U (-1:2) U (2:+oo)

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

1/(x^2+3*x+2)-(1/(x-2))-(2/(x^2-4)) = 0

1/(x^2+3*x+2)-(x-2)^-1-2*(x^2-4)^-1 = 0

1/(x^2+3*x+2)-1/(x-2)-2/(x^2-4) = 0

x^2+3*x+2 = 0

x^2+3*x+2 = 0

x^2+3*x+2 = 0

DELTA = 3^2-(1*2*4)

DELTA = 1

DELTA > 0

x = (1^(1/2)-3)/(1*2) or x = (-1^(1/2)-3)/(1*2)

x = -1 or x = -2

(x+2)*(x+1) = 0

1/((x+2)*(x+1))-1/(x-2)-2/(x^2-4) = 0

(1*(x-2)*(x^2-4))/((x+2)*(x+1)*(x-2)*(x^2-4))+(-1*(x+2)*(x+1)*(x^2-4))/((x+2)*(x+1)*(x-2)*(x^2-4))+(-2*(x+2)*(x+1)*(x-2))/((x+2)*(x+1)*(x-2)*(x^2-4)) = 0

1*(x-2)*(x^2-4)-1*(x+2)*(x+1)*(x^2-4)-2*(x+2)*(x+1)*(x-2) = 0

8*x-x^4-2*x^3-2*x^3-2*x^2+8*x+8+16 = 0

16*x-x^4-4*x^3-2*x^2+24 = 0

16*x-x^4-4*x^3-2*x^2+24 = 0

16*x-x^4-4*x^3-2*x^2+24 = 0

{ 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 8, -8, 12, -12, 24, -24 }

1

x = 1

16*x-x^4-4*x^3-2*x^2+24 = 33

1

-1

x = -1

16*x-x^4-4*x^3-2*x^2+24 = 9

-1

2

x = 2

16*x-x^4-4*x^3-2*x^2+24 = 0

2

x-2

-x^3-6*x^2-14*x-12

16*x-x^4-4*x^3-2*x^2+24

x-2

x^4-2*x^3

16*x-6*x^3-2*x^2+24

6*x^3-12*x^2

16*x-14*x^2+24

14*x^2-28*x

24-12*x

12*x-24

0

-x^3-6*x^2-14*x-12 = 0

{ 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 12, -12 }

1

x = 1

-x^3-6*x^2-14*x-12 = -33

1

-1

x = -1

-x^3-6*x^2-14*x-12 = -3

-1

2

x = 2

-x^3-6*x^2-14*x-12 = -72

2

-2

x = -2

-x^3-6*x^2-14*x-12 = 0

-2

x+2

-x^2-4*x-6

-x^3-6*x^2-14*x-12

x+2

x^3+2*x^2

-4*x^2-14*x-12

4*x^2+8*x

-6*x-12

6*x+12

0

-x^2-4*x-6 = 0

DELTA = (-4)^2-(-6*(-1)*4)

DELTA = -8

DELTA < 0

x in { 2, -2} 

(x-2)*(x+2) = 0

((x-2)*(x+2))/((x+2)*(x+1)*(x-2)*(x^2-4)) = 0

((x-2)*(x+2))/((x+2)*(x+1)*(x-2)*(x^2-4)) = 0 // * (x+2)*(x+1)*(x-2)*(x^2-4)

(x-2)*(x+2) = 0

( x+2 )

x+2 = 0 // - 2

x = -2

( x-2 )

x-2 = 0 // + 2

x = 2

x in { -2} 

x in { 2} 

x belongs to the empty set

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