(2)/(3x+6)=(x+2)/(x^2-10)

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Solution for (2)/(3x+6)=(x+2)/(x^2-10) equation: 


D( x )

3*x+6 = 0

x^2-10 = 0

3*x+6 = 0

3*x+6 = 0

3*x+6 = 0 // - 6

3*x = -6 // : 3

x = -6/3

x = -2

x^2-10 = 0

x^2-10 = 0

1*x^2 = 10 // : 1

x^2 = 10

x^2 = 10 // ^ 1/2

abs(x) = 10^(1/2)

x = 10^(1/2) or x = -10^(1/2)

x in (-oo:-10^(1/2)) U (-10^(1/2):-2) U (-2:10^(1/2)) U (10^(1/2):+oo)

2/(3*x+6) = (x+2)/(x^2-10) // - (x+2)/(x^2-10)

2/(3*x+6)-((x+2)/(x^2-10)) = 0

2/(3*x+6)+(-1*(x+2))/(x^2-10) = 0

(2*(x^2-10))/((3*x+6)*(x^2-10))+(-1*(x+2)*(3*x+6))/((3*x+6)*(x^2-10)) = 0

2*(x^2-10)-1*(x+2)*(3*x+6) = 0

-x^2-12*x-32 = 0

-x^2-12*x-32 = 0

-1*(x^2+12*x+32) = 0

x^2+12*x+32 = 0

DELTA = 12^2-(1*4*32)

DELTA = 16

DELTA > 0

x = (16^(1/2)-12)/(1*2) or x = (-16^(1/2)-12)/(1*2)

x = -4 or x = -8

-1*(x+8)*(x+4) = 0

(-1*(x+8)*(x+4))/((3*x+6)*(x^2-10)) = 0

(-1*(x+8)*(x+4))/((3*x+6)*(x^2-10)) = 0 // * (3*x+6)*(x^2-10)

-1*(x+8)*(x+4) = 0

( x+4 )

x+4 = 0 // - 4

x = -4

( x+8 )

x+8 = 0 // - 8

x = -8

x in { -4, -8 }

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