(7x-6)/(9x^2-4)=(-3x^2+3x-2)/(9x^2-4)+(x+2)/(3x+2)

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Solution for (7x-6)/(9x^2-4)=(-3x^2+3x-2)/(9x^2-4)+(x+2)/(3x+2) equation: 


D( x )

9*x^2-4 = 0

3*x+2 = 0

9*x^2-4 = 0

9*x^2-4 = 0

9*x^2 = 4 // : 9

x^2 = 4/9

x^2 = 4/9 // ^ 1/2

abs(x) = 2/3

x = 2/3 or x = -2/3

3*x+2 = 0

3*x+2 = 0

3*x+2 = 0 // - 2

3*x = -2 // : 3

x = -2/3

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

(7*x-6)/(9*x^2-4) = (3*x-3*x^2-2)/(9*x^2-4)+(x+2)/(3*x+2) // - (3*x-3*x^2-2)/(9*x^2-4)+(x+2)/(3*x+2)

(7*x-6)/(9*x^2-4)-((3*x-3*x^2-2)/(9*x^2-4))-((x+2)/(3*x+2)) = 0

(7*x-6)/(9*x^2-4)+(-1*(3*x-3*x^2-2))/(9*x^2-4)+(-1*(x+2))/(3*x+2) = 0

((7*x-6)*(3*x+2))/((9*x^2-4)*(3*x+2))+(-1*(3*x-3*x^2-2)*(3*x+2))/((9*x^2-4)*(3*x+2))+(-1*(x+2)*(9*x^2-4))/((9*x^2-4)*(3*x+2)) = 0

(7*x-6)*(3*x+2)-1*(3*x-3*x^2-2)*(3*x+2)-1*(x+2)*(9*x^2-4) = 0

9*x^3-9*x^3+18*x^2-18*x^2-4*x+4*x-8+8 = 0

0 = 0

0/((9*x^2-4)*(3*x+2)) = 0

0/((9*x^2-4)*(3*x+2)) = 0 // * (9*x^2-4)*(3*x+2)

0 = 0

x belongs to the empty set

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