(16x-11)/(25x^2-9)=(-5x^2+4x-2)/(25x^2-9)+(x+3)/(5x+3)

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Solution for (16x-11)/(25x^2-9)=(-5x^2+4x-2)/(25x^2-9)+(x+3)/(5x+3) equation: 


D( x )

25*x^2-9 = 0

5*x+3 = 0

25*x^2-9 = 0

25*x^2-9 = 0

25*x^2 = 9 // : 25

x^2 = 9/25

x^2 = 9/25 // ^ 1/2

abs(x) = 3/5

x = 3/5 or x = -3/5

5*x+3 = 0

5*x+3 = 0

5*x+3 = 0 // - 3

5*x = -3 // : 5

x = -3/5

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

(16*x-11)/(25*x^2-9) = (4*x-5*x^2-2)/(25*x^2-9)+(x+3)/(5*x+3) // - (4*x-5*x^2-2)/(25*x^2-9)+(x+3)/(5*x+3)

(16*x-11)/(25*x^2-9)-((4*x-5*x^2-2)/(25*x^2-9))-((x+3)/(5*x+3)) = 0

(16*x-11)/(25*x^2-9)+(-1*(4*x-5*x^2-2))/(25*x^2-9)+(-1*(x+3))/(5*x+3) = 0

((16*x-11)*(5*x+3))/((25*x^2-9)*(5*x+3))+(-1*(4*x-5*x^2-2)*(5*x+3))/((25*x^2-9)*(5*x+3))+(-1*(x+3)*(25*x^2-9))/((25*x^2-9)*(5*x+3)) = 0

(16*x-11)*(5*x+3)-1*(4*x-5*x^2-2)*(5*x+3)-1*(x+3)*(25*x^2-9) = 0

25*x^3-25*x^3+75*x^2-75*x^2-9*x+9*x-27+27 = 0

0 = 0

0/((25*x^2-9)*(5*x+3)) = 0

0/((25*x^2-9)*(5*x+3)) = 0 // * (25*x^2-9)*(5*x+3)

0 = 0

x belongs to the empty set

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