(5/x)+(x/x+2)=4/(x^2+2x)

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Solution for (5/x)+(x/x+2)=4/(x^2+2x) equation: 


D( x )

x = 0

x^2+2*x = 0

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)

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

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

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

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

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

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

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

x^2+2*x^2+5*x+2*x+4*x+6 = 0

x^2+2*x^2+7*x+4*x+6 = 0

3*x^2+11*x+6 = 0

3*x^2+11*x+6 = 0

3*x^2+11*x+6 = 0

DELTA = 11^2-(3*4*6)

DELTA = 49

DELTA > 0

x = (49^(1/2)-11)/(2*3) or x = (-49^(1/2)-11)/(2*3)

x = -2/3 or x = -3

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

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

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

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

( x+2/3 )

x+2/3 = 0 // - 2/3

x = -2/3

( x+3 )

x+3 = 0 // - 3

x = -3

x in { -2/3, -3 }

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