((x^2-9)/(x^2+7x+12))/((x^2-4x-32)/(x^2-3x))

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Solution for ((x^2-9)/(x^2+7x+12))/((x^2-4x-32)/(x^2-3x)) equation: 


D( x )

(x^2-(4*x)-32)/(x^2-(3*x)) = 0

x^2-(3*x) = 0

x^2+7*x+12 = 0

(x^2-(4*x)-32)/(x^2-(3*x)) = 0

(x^2-(4*x)-32)/(x^2-(3*x)) = 0

(x^2-4*x-32)/(x^2-3*x) = 0

x^2-4*x-32 = 0

x^2-4*x-32 = 0

DELTA = (-4)^2-(-32*1*4)

DELTA = 144

DELTA > 0

x = (144^(1/2)+4)/(1*2) or x = (4-144^(1/2))/(1*2)

x = 8 or x = -4

(x+4)*(x-8) = 0

x^2-3*x = 0

x*(x-3) = 0

x-3 = 0 // + 3

x = 3

x*(x-3) = 0

((x+4)*(x-8))/(x*(x-3)) = 0

( x+4 )

x+4 = 0 // - 4

x = -4

( x-8 )

x-8 = 0 // + 8

x = 8

x^2-(3*x) = 0

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

x = 3 or x = 0

x^2+7*x+12 = 0

x^2+7*x+12 = 0

x^2+7*x+12 = 0

DELTA = 7^2-(1*4*12)

DELTA = 1

DELTA > 0

x = (1^(1/2)-7)/(1*2) or x = (-1^(1/2)-7)/(1*2)

x = -3 or x = -4

x in (-oo:-4) U (-4:-3) U (-3:0) U (0:3) U (3:8) U (8:+oo)

((x^2-9)/(x^2+7*x+12))/((x^2-(4*x)-32)/(x^2-(3*x))) = 0

((x^2-9)/(x^2+7*x+12))/((x^2-4*x-32)/(x^2-3*x)) = 0

((x^2-9)*(x^2-3*x))/((x^2+7*x+12)*(x^2-4*x-32)) = 0

x^2+7*x+12 = 0

x^2+7*x+12 = 0

DELTA = 7^2-(1*4*12)

DELTA = 1

DELTA > 0

x = (1^(1/2)-7)/(1*2) or x = (-1^(1/2)-7)/(1*2)

x = -3 or x = -4

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

x^2-4*x-32 = 0

x^2-4*x-32 = 0

DELTA = (-4)^2-(-32*1*4)

DELTA = 144

DELTA > 0

x = (144^(1/2)+4)/(1*2) or x = (4-144^(1/2))/(1*2)

x = 8 or x = -4

(x+4)*(x-8) = 0

x^2-3*x = 0

x*(x-3) = 0

x-3 = 0 // + 3

x = 3

x*(x-3) = 0

(x*(x^2-9)*(x-3))/((x+4)^2*(x+3)*(x-8)) = 0

( x-3 )

x-3 = 0 // + 3

x = 3

( x )

x = 0

( x^2-9 )

1*x^2 = 9 // : 1

x^2 = 9

x^2 = 9 // ^ 1/2

abs(x) = 3

x = 3 or x = -3

x in { 3} 

x in { 0} 

x in { 3} 

x in { -3} 

x belongs to the empty set

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