(9x^2-12x)/(x^2+1)((2x^2+2)/(9x^2+6x-24))

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Solution for (9x^2-12x)/(x^2+1)((2x^2+2)/(9x^2+6x-24)) equation:


D( x )

9*x^2+6*x-24 = 0

x^2+1 = 0

9*x^2+6*x-24 = 0

9*x^2+6*x-24 = 0

9*x^2+6*x-24 = 0

DELTA = 6^2-(-24*4*9)

DELTA = 900

DELTA > 0

x = (900^(1/2)-6)/(2*9) or x = (-900^(1/2)-6)/(2*9)

x = 4/3 or x = -2

x^2+1 = 0

x^2+1 = 0

1*x^2 = -1 // : 1

x^2 = -1

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

((9*x^2-(12*x))/(x^2+1))*((2*x^2+2)/(9*x^2+6*x-24)) = 0

((9*x^2-12*x)/(x^2+1))*((2*x^2+2)/(9*x^2+6*x-24)) = 0

((9*x^2-12*x)*(2*x^2+2))/((x^2+1)*(9*x^2+6*x-24)) = 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-24 = 0

3*(3*x^2+2*x-8) = 0

3*x^2+2*x-8 = 0

DELTA = 2^2-(-8*3*4)

DELTA = 100

DELTA > 0

x = (100^(1/2)-2)/(2*3) or x = (-100^(1/2)-2)/(2*3)

x = 4/3 or x = -2

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

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

( 2*x^2+2 )

2*x^2 = -2 // : 2

x^2 = -1

( 3*x )

3*x = 0 // : 3

x = 0

( x-4/3 )

x-4/3 = 0 // + 4/3

x = 4/3

x in { 4/3}

x = 0

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