((3+p)/(2-p))+((1+2p)/(1+3p+2p^2))

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Solution for ((3+p)/(2-p))+((1+2p)/(1+3p+2p^2)) equation: 


D( p )

2*p^2+3*p+1 = 0

2-p = 0

2*p^2+3*p+1 = 0

2*p^2+3*p+1 = 0

2*p^2+3*p+1 = 0

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

DELTA = 1

DELTA > 0

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

p = -1/2 or p = -1

2-p = 0

2-p = 0

2-p = 0 // - 2

-p = -2 // * -1

p = 2

p in (-oo:-1) U (-1:-1/2) U (-1/2:2) U (2:+oo)

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

2*p^2+3*p+1 = 0

2*p^2+3*p+1 = 0

2*p^2+3*p+1 = 0

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

DELTA = 1

DELTA > 0

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

p = -1/2 or p = -1

(p+1)*(p+1/2) = 0

(p+3)/(2-p)+(2*p+1)/((p+1)*(p+1/2)) = 0

((p+3)*(p+1)*(p+1/2))/((2-p)*(p+1)*(p+1/2))+((2*p+1)*(2-p))/((2-p)*(p+1)*(p+1/2)) = 0

(p+3)*(p+1)*(p+1/2)+(2*p+1)*(2-p) = 0

p^3+5/2*p^2+8*p+7/2 = 0

p^3+5/2*p^2+8*p+7/2 = 0

p^3+(5/2)*p^2+8*p+7/2 = 0

p^3+(5/2)*p^2+8*p+7/2 = 0 // * 0

{ 1, -1, 7, -7 }

1

p = 1

2*p^3+5*p^2+16*p+7 = 30

1

-1

p = -1

2*p^3+5*p^2+16*p+7 = -6

-1

7

p = 7

2*p^3+5*p^2+16*p+7 = 1050

7

-7

p = -7

2*p^3+5*p^2+16*p+7 = -546

-7

{ 1/2, -1/2, -1/2, 1/2, 7/2, -7/2, -7/2, 7/2 }

1/2

p

1/2

2*p^3+5*p^2+16*p+7 = 16.5

1/2

-1/2

p

-1/2

2*p^3+5*p^2+16*p+7 = 0

-1/2

p+1/2

2*p^2+4*p+14

2*p^3+5*p^2+16*p+7

p+1/2

-2*p^3-p^2

4*p^2+16*p+7

-4*p^2-2*p

14*p+7

-14*p-7

0

2*p^2+4*p+14 = 0

DELTA = 4^2-(2*4*14)

DELTA = -96

DELTA < 0

p in { -1/2} 

p+1/2 = 0

(p+1/2)/((2-p)*(p+1)*(p+1/2)) = 0

(p+1/2)/((2-p)*(p+1)*(p+1/2)) = 0 // * (2-p)*(p+1)*(p+1/2)

p+1/2 = 0

p+1/2 = 0 // - 1/2

p = -1/2

p in { -1/2} 

p belongs to the empty set

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