((3x^2-5x-2)/(x^2+3x))*((x^2-3x)/(3x^2-8x-3))

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Solution for ((3x^2-5x-2)/(x^2+3x))*((x^2-3x)/(3x^2-8x-3)) equation:


D( x )

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

x^2+3*x = 0

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

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

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

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

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

DELTA = 100

DELTA > 0

x = (100^(1/2)+8)/(2*3) or x = (8-100^(1/2))/(2*3)

x = 3 or x = -1/3

x^2+3*x = 0

x^2+3*x = 0

x^2+3*x = 0

DELTA = 3^2-(0*1*4)

DELTA = 9

DELTA > 0

x = (9^(1/2)-3)/(1*2) or x = (-9^(1/2)-3)/(1*2)

x = 0 or x = -3

x in (-oo:-3) U (-3:-1/3) U (-1/3:0) U (0:3) U (3:+oo)

((3*x^2-(5*x)-2)/(x^2+3*x))*((x^2-(3*x))/(3*x^2-(8*x)-3)) = 0

((3*x^2-5*x-2)/(x^2+3*x))*((x^2-3*x)/(3*x^2-8*x-3)) = 0

((3*x^2-5*x-2)*(x^2-3*x))/((x^2+3*x)*(3*x^2-8*x-3)) = 0

3*x^2-5*x-2 = 0

3*x^2-5*x-2 = 0

DELTA = (-5)^2-(-2*3*4)

DELTA = 49

DELTA > 0

x = (49^(1/2)+5)/(2*3) or x = (5-49^(1/2))/(2*3)

x = 2 or x = -1/3

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

x^2+3*x = 0

x*(x+3) = 0

x+3 = 0 // - 3

x = -3

x*(x+3) = 0

x^2-3*x = 0

x*(x-3) = 0

x-3 = 0 // + 3

x = 3

x*(x-3) = 0

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

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

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

DELTA = 100

DELTA > 0

x = (100^(1/2)+8)/(2*3) or x = (8-100^(1/2))/(2*3)

x = 3 or x = -1/3

(x+1/3)*(x-3) = 0

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

( x+1/3 )

x+1/3 = 0 // - 1/3

x = -1/3

( x-2 )

x-2 = 0 // + 2

x = 2

( x-3 )

x-3 = 0 // + 3

x = 3

( x )

x = 0

x in { -1/3}

x in { 3}

x in { 0}

x = 2

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