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

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


D( x )

x+2 = 0

x = 0

x^2+2*x = 0

x+2 = 0

x+2 = 0

x+2 = 0 // - 2

x = -2

x = 0

x = 0

x^2+2*x = 0

x^2+2*x = 0

x^2+2*x = 0

DELTA = 2^2-(0*1*4)

DELTA = 4

DELTA > 0

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

x = 0 or x = -2

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

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

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

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

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

x^2+2*x = 0

x^2+2*x = 0

x*(x+2) = 0

x+2 = 0 // - 2

x = -2

x*(x+2) = 0

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

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

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

x^2-4*x^2+x-8*x-4+2 = 0

x^2-4*x^2+x-8*x-2 = 0

-3*x^2-7*x-2 = 0

-3*x^2-7*x-2 = 0

-1*(3*x^2+7*x+2) = 0

3*x^2+7*x+2 = 0

DELTA = 7^2-(2*3*4)

DELTA = 25

DELTA > 0

x = (25^(1/2)-7)/(2*3) or x = (-25^(1/2)-7)/(2*3)

x = -1/3 or x = -2

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

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

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

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

( x+1/3 )

x+1/3 = 0 // - 1/3

x = -1/3

( x+2 )

x+2 = 0 // - 2

x = -2

x in { -2} 

x = -1/3

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