5/(9x^2+18x+8)=10/(9x^2+12x)-1/(9x^2+6x)

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Solution for 5/(9x^2+18x+8)=10/(9x^2+12x)-1/(9x^2+6x) equation: 


D( x )

9*x^2+6*x = 0

9*x^2+12*x = 0

9*x^2+18*x+8 = 0

9*x^2+6*x = 0

9*x^2+6*x = 0

9*x^2+6*x = 0

DELTA = 6^2-(0*4*9)

DELTA = 36

DELTA > 0

x = (36^(1/2)-6)/(2*9) or x = (-36^(1/2)-6)/(2*9)

x = 0 or x = -2/3

9*x^2+12*x = 0

9*x^2+12*x = 0

9*x^2+12*x = 0

DELTA = 12^2-(0*4*9)

DELTA = 144

DELTA > 0

x = (144^(1/2)-12)/(2*9) or x = (-144^(1/2)-12)/(2*9)

x = 0 or x = -4/3

9*x^2+18*x+8 = 0

9*x^2+18*x+8 = 0

9*x^2+18*x+8 = 0

DELTA = 18^2-(4*8*9)

DELTA = 36

DELTA > 0

x = (36^(1/2)-18)/(2*9) or x = (-36^(1/2)-18)/(2*9)

x = -2/3 or x = -4/3

x in (-oo:-4/3) U (-4/3:-2/3) U (-2/3:0) U (0:+oo)

5/(9*x^2+18*x+8) = 10/(9*x^2+12*x)-(1/(9*x^2+6*x)) // - 10/(9*x^2+12*x)-(1/(9*x^2+6*x))

5/(9*x^2+18*x+8)-(10/(9*x^2+12*x))+1/(9*x^2+6*x) = 0

5/(9*x^2+18*x+8)-10*(9*x^2+12*x)^-1+1/(9*x^2+6*x) = 0

5/(9*x^2+18*x+8)-10/(9*x^2+12*x)+1/(9*x^2+6*x) = 0

9*x^2+18*x+8 = 0

9*x^2+18*x+8 = 0

9*x^2+18*x+8 = 0

DELTA = 18^2-(4*8*9)

DELTA = 36

DELTA > 0

x = (36^(1/2)-18)/(2*9) or x = (-36^(1/2)-18)/(2*9)

x = -2/3 or x = -4/3

(x+4/3)*(x+2/3) = 0

9*x^2+12*x = 0

9*x^2+12*x = 0

3*x*(3*x+4) = 0

3*x+4 = 0 // - 4

3*x = -4 // : 3

x = -4/3

3*x*(x+4/3) = 0

9*x^2+6*x = 0

9*x^2+6*x = 0

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

3*x+2 = 0 // - 2

3*x = -2 // : 3

x = -2/3

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

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

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

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

5*x+x-20/3+4/3 = 0

6*x-16/3 = 0

(6*x-16/3)/(3*x*(x+4/3)*(x+2/3)) = 0

(6*x-16/3)/(3*x*(x+4/3)*(x+2/3)) = 0 // * 3*x*(x+4/3)*(x+2/3)

6*x-16/3 = 0

6*x-16/3 = 0 // + 16/3

6*x = 16/3 // : 6

x = 16/3/6

x = 8/9

x = 8/9

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