(2x)/(x+3)+(5)/(x)-4=(18)/(x^2+3x)

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Solution for (2x)/(x+3)+(5)/(x)-4=(18)/(x^2+3x) equation: 


D( x )

x^2+3*x = 0

x = 0

x+3 = 0

x^2+3*x = 0

x^2+3*x = 0

x^2+3*x = 0

DELTA = 3^2-(0*1*4)

DELTA = 9

DELTA > 0

x = (9^(1/2)-3)/(1*2) or x = (-9^(1/2)-3)/(1*2)

x = 0 or x = -3

x = 0

x = 0

x+3 = 0

x+3 = 0

x+3 = 0 // - 3

x = -3

x in (-oo:-3) U (-3:0) U (0:+oo)

(2*x)/(x+3)+5/x-4 = 18/(x^2+3*x) // - 18/(x^2+3*x)

(2*x)/(x+3)-(18/(x^2+3*x))+5/x-4 = 0

(2*x)/(x+3)-18*(x^2+3*x)^-1+5/x-4 = 0

(2*x)/(x+3)-18/(x^2+3*x)+5/x-4 = 0

x^2+3*x = 0

x^2+3*x = 0

x*(x+3) = 0

x+3 = 0 // - 3

x = -3

x*(x+3) = 0

(2*x)/(x+3)-18/(x*(x+3))+5/x-4 = 0

(2*x*x)/(x*(x+3))-18/(x*(x+3))+(5*(x+3))/(x*(x+3))+(-4*x*(x+3))/(x*(x+3)) = 0

5*(x+3)-4*x*(x+3)+2*x*x-18 = 0

2*x^2-4*x^2+5*x-12*x-18+15 = 0

2*x^2-4*x^2+5*x-12*x-3 = 0

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

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

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

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

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

DELTA = 25

DELTA > 0

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

x = -1/2 or x = -3

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

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

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

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

( x+1/2 )

x+1/2 = 0 // - 1/2

x = -1/2

( x+3 )

x+3 = 0 // - 3

x = -3

x in { -3} 

x = -1/2

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