(2/(x^2+2x-8))+(5/(x^2+x-6))=(1/(x^2+7x+12))

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Solution for (2/(x^2+2x-8))+(5/(x^2+x-6))=(1/(x^2+7x+12)) equation: 


D( x )

x^2+7*x+12 = 0

x^2+x-6 = 0

x^2+2*x-8 = 0

x^2+7*x+12 = 0

x^2+7*x+12 = 0

x^2+7*x+12 = 0

DELTA = 7^2-(1*4*12)

DELTA = 1

DELTA > 0

x = (1^(1/2)-7)/(1*2) or x = (-1^(1/2)-7)/(1*2)

x = -3 or x = -4

x^2+x-6 = 0

x^2+x-6 = 0

x^2+x-6 = 0

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

DELTA = 25

DELTA > 0

x = (25^(1/2)-1)/(1*2) or x = (-25^(1/2)-1)/(1*2)

x = 2 or x = -3

x^2+2*x-8 = 0

x^2+2*x-8 = 0

x^2+2*x-8 = 0

DELTA = 2^2-(-8*1*4)

DELTA = 36

DELTA > 0

x = (36^(1/2)-2)/(1*2) or x = (-36^(1/2)-2)/(1*2)

x = 2 or x = -4

x in (-oo:-4) U (-4:-3) U (-3:2) U (2:+oo)

2/(x^2+2*x-8)+5/(x^2+x-6) = 1/(x^2+7*x+12) // - 1/(x^2+7*x+12)

2/(x^2+2*x-8)+5/(x^2+x-6)-(1/(x^2+7*x+12)) = 0

2/(x^2+2*x-8)+5/(x^2+x-6)-(x^2+7*x+12)^-1 = 0

2/(x^2+2*x-8)+5/(x^2+x-6)-1/(x^2+7*x+12) = 0

x^2+2*x-8 = 0

x^2+2*x-8 = 0

x^2+2*x-8 = 0

DELTA = 2^2-(-8*1*4)

DELTA = 36

DELTA > 0

x = (36^(1/2)-2)/(1*2) or x = (-36^(1/2)-2)/(1*2)

x = 2 or x = -4

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

x^2+x-6 = 0

x^2+x-6 = 0

x^2+x-6 = 0

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

DELTA = 25

DELTA > 0

x = (25^(1/2)-1)/(1*2) or x = (-25^(1/2)-1)/(1*2)

x = 2 or x = -3

(x+3)*(x-2) = 0

x^2+7*x+12 = 0

x^2+7*x+12 = 0

x^2+7*x+12 = 0

DELTA = 7^2-(1*4*12)

DELTA = 1

DELTA > 0

x = (1^(1/2)-7)/(1*2) or x = (-1^(1/2)-7)/(1*2)

x = -3 or x = -4

(x+4)*(x+3) = 0

2/((x+4)*(x-2))+5/((x+3)*(x-2))-1/((x+4)*(x+3)) = 0

(2*(x+3))/((x+4)*(x-2)*(x+3))+(5*(x+4))/((x+4)*(x-2)*(x+3))+(-1*(x-2))/((x+4)*(x-2)*(x+3)) = 0

2*(x+3)+5*(x+4)-1*(x-2) = 0

7*x-x+2+26 = 0

6*x+28 = 0

(6*x+28)/((x+4)*(x-2)*(x+3)) = 0

(6*x+28)/((x+4)*(x-2)*(x+3)) = 0 // * (x+4)*(x-2)*(x+3)

6*x+28 = 0

6*x+28 = 0 // - 28

6*x = -28 // : 6

x = -28/6

x = -14/3

x = -14/3

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