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

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


D( x )

x+2 = 0

x = 0

x+1 = 0

x+2 = 0

x+2 = 0

x+2 = 0 // - 2

x = -2

x = 0

x = 0

x+1 = 0

x+1 = 0

x+1 = 0 // - 1

x = -1

x in (-oo:-2) U (-2:-1) U (-1:0) U (0:+oo)

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

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

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

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

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

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

3*x^2-2*x^2+9*x+6 = 0

x^2+9*x+6 = 0

x^2+9*x+6 = 0

x^2+9*x+6 = 0

DELTA = 9^2-(1*4*6)

DELTA = 57

DELTA > 0

x = (57^(1/2)-9)/(1*2) or x = (-57^(1/2)-9)/(1*2)

x = (57^(1/2)-9)/2 or x = (-(57^(1/2)+9))/2

(x+(57^(1/2)+9)/2)*(x-((57^(1/2)-9)/2)) = 0

((x+(57^(1/2)+9)/2)*(x-((57^(1/2)-9)/2)))/(x*(x+1)*(x+2)) = 0

((x+(57^(1/2)+9)/2)*(x-((57^(1/2)-9)/2)))/(x*(x+1)*(x+2)) = 0 // * x*(x+1)*(x+2)

(x+(57^(1/2)+9)/2)*(x-((57^(1/2)-9)/2)) = 0

( x+(57^(1/2)+9)/2 )

x+(57^(1/2)+9)/2 = 0 // - (57^(1/2)+9)/2

x = -((57^(1/2)+9)/2)

( x-((57^(1/2)-9)/2) )

x-((57^(1/2)-9)/2) = 0 // + (57^(1/2)-9)/2

x = (57^(1/2)-9)/2

x in { -((57^(1/2)+9)/2), (57^(1/2)-9)/2 }

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