((2x+1)/(x-3))-((x-4)/(x+5))=-((10x+13)/(x+5))

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Solution for ((2x+1)/(x-3))-((x-4)/(x+5))=-((10x+13)/(x+5)) equation: 


D( x )

x+5 = 0

x-3 = 0

x+5 = 0

x+5 = 0

x+5 = 0 // - 5

x = -5

x-3 = 0

x-3 = 0

x-3 = 0 // + 3

x = 3

x in (-oo:-5) U (-5:3) U (3:+oo)

(2*x+1)/(x-3)-((x-4)/(x+5)) = -((10*x+13)/(x+5)) // + (10*x+13)/(x+5)

(2*x+1)/(x-3)-((x-4)/(x+5))+(10*x+13)/(x+5) = 0

(2*x+1)/(x-3)+(-1*(x-4))/(x+5)+(10*x+13)/(x+5) = 0

((2*x+1)*(x+5))/((x-3)*(x+5))+(-1*(x-4)*(x-3))/((x-3)*(x+5))+((10*x+13)*(x-3))/((x-3)*(x+5)) = 0

(2*x+1)*(x+5)-1*(x-4)*(x-3)+(10*x+13)*(x-3) = 0

x^2+10*x^2+18*x-17*x-39-7 = 0

11*x^2+x-46 = 0

11*x^2+x-46 = 0

11*x^2+x-46 = 0

DELTA = 1^2-(-46*4*11)

DELTA = 2025

DELTA > 0

x = (2025^(1/2)-1)/(2*11) or x = (-2025^(1/2)-1)/(2*11)

x = 2 or x = -23/11

(x+23/11)*(x-2) = 0

((x+23/11)*(x-2))/((x-3)*(x+5)) = 0

((x+23/11)*(x-2))/((x-3)*(x+5)) = 0 // * (x-3)*(x+5)

(x+23/11)*(x-2) = 0

( x+23/11 )

x+23/11 = 0 // - 23/11

x = -23/11

( x-2 )

x-2 = 0 // + 2

x = 2

x in { -23/11, 2 }

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