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

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


D( x )

x+4 = 0

x+2 = 0

x+1 = 0

x+4 = 0

x+4 = 0

x+4 = 0 // - 4

x = -4

x+2 = 0

x+2 = 0

x+2 = 0 // - 2

x = -2

x+1 = 0

x+1 = 0

x+1 = 0 // - 1

x = -1

x in (-oo:-4) U (-4:-2) U (-2:-1) U (-1:+oo)

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

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

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

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

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

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

3*x^2-4*x^2+16*x-12*x-8+16 = 0

4*x-x^2+8 = 0

4*x-x^2+8 = 0

4*x-x^2+8 = 0

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

DELTA = 48

DELTA > 0

x = (48^(1/2)-4)/(-1*2) or x = (-48^(1/2)-4)/(-1*2)

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

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

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

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

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

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

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

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

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

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

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

x in { (-4*3^(1/2)-4)/(-2), (4*3^(1/2)-4)/(-2) }

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