(2x)/(x-2)+(x)/(x+3)=(-5)/(x+3)

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


D( x )

x-2 = 0

x+3 = 0

x-2 = 0

x-2 = 0

x-2 = 0 // + 2

x = 2

x+3 = 0

x+3 = 0

x+3 = 0 // - 3

x = -3

x in (-oo:-3) U (-3:2) U (2:+oo)

(2*x)/(x-2)+x/(x+3) = -5/(x+3) // + -5/(x+3)

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

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

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

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

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

3*x^2+4*x+5*x-10 = 0

3*x^2+9*x-10 = 0

3*x^2+9*x-10 = 0

3*x^2+9*x-10 = 0

DELTA = 9^2-(-10*3*4)

DELTA = 201

DELTA > 0

x = (201^(1/2)-9)/(2*3) or x = (-201^(1/2)-9)/(2*3)

x = (201^(1/2)-9)/6 or x = (-(201^(1/2)+9))/6

(x+(201^(1/2)+9)/6)*(x-((201^(1/2)-9)/6)) = 0

((x+(201^(1/2)+9)/6)*(x-((201^(1/2)-9)/6)))/((x-2)*(x+3)) = 0

((x+(201^(1/2)+9)/6)*(x-((201^(1/2)-9)/6)))/((x-2)*(x+3)) = 0 // * (x-2)*(x+3)

(x+(201^(1/2)+9)/6)*(x-((201^(1/2)-9)/6)) = 0

( x+(201^(1/2)+9)/6 )

x+(201^(1/2)+9)/6 = 0 // - (201^(1/2)+9)/6

x = -((201^(1/2)+9)/6)

( x-((201^(1/2)-9)/6) )

x-((201^(1/2)-9)/6) = 0 // + (201^(1/2)-9)/6

x = (201^(1/2)-9)/6

x in { -((201^(1/2)+9)/6), (201^(1/2)-9)/6 }

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