(2x-5)/(x)+(4x-1)/(x+2)=(3x+8)/(x^2+2x)

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Solution for (2x-5)/(x)+(4x-1)/(x+2)=(3x+8)/(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)

(2*x-5)/x+(4*x-1)/(x+2) = (3*x+8)/(x^2+2*x) // - (3*x+8)/(x^2+2*x)

(2*x-5)/x+(4*x-1)/(x+2)-((3*x+8)/(x^2+2*x)) = 0

(2*x-5)/x+(4*x-1)/(x+2)+(-1*(3*x+8))/(x^2+2*x) = 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

(2*x-5)/x+(4*x-1)/(x+2)+(-1*(3*x+8))/(x*(x+2)) = 0

((2*x-5)*(x+2))/(x*(x+2))+(x*(4*x-1))/(x*(x+2))+(-1*(3*x+8))/(x*(x+2)) = 0

(2*x-5)*(x+2)+x*(4*x-1)-1*(3*x+8) = 0

6*x^2-2*x-3*x-10-8 = 0

6*x^2-5*x-18 = 0

6*x^2-5*x-18 = 0

6*x^2-5*x-18 = 0

DELTA = (-5)^2-(-18*4*6)

DELTA = 457

DELTA > 0

x = (457^(1/2)+5)/(2*6) or x = (5-457^(1/2))/(2*6)

x = (457^(1/2)+5)/12 or x = (5-457^(1/2))/12

(x-((5-457^(1/2))/12))*(x-((457^(1/2)+5)/12)) = 0

((x-((5-457^(1/2))/12))*(x-((457^(1/2)+5)/12)))/(x*(x+2)) = 0

((x-((5-457^(1/2))/12))*(x-((457^(1/2)+5)/12)))/(x*(x+2)) = 0 // * x*(x+2)

(x-((5-457^(1/2))/12))*(x-((457^(1/2)+5)/12)) = 0

( x-((457^(1/2)+5)/12) )

x-((457^(1/2)+5)/12) = 0 // + (457^(1/2)+5)/12

x = (457^(1/2)+5)/12

( x-((5-457^(1/2))/12) )

x-((5-457^(1/2))/12) = 0 // + (5-457^(1/2))/12

x = (5-457^(1/2))/12

x in { (457^(1/2)+5)/12, (5-457^(1/2))/12 }

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