(x^2-81)/(x^2-6x-27)*(x+3)/x

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Solution for (x^2-81)/(x^2-6x-27)*(x+3)/x equation: 


D( x )

x = 0

x^2-(6*x)-27 = 0

x = 0

x = 0

x^2-(6*x)-27 = 0

x^2-(6*x)-27 = 0

x^2-6*x-27 = 0

x^2-6*x-27 = 0

DELTA = (-6)^2-(-27*1*4)

DELTA = 144

DELTA > 0

x = (144^(1/2)+6)/(1*2) or x = (6-144^(1/2))/(1*2)

x = 9 or x = -3

x in (-oo:-3) U (-3:0) U (0:9) U (9:+oo)

(((x^2-81)/(x^2-(6*x)-27))*(x+3))/x = 0

(((x^2-81)/(x^2-6*x-27))*(x+3))/x = 0

((x^2-81)*(x+3))/(x*(x^2-6*x-27)) = 0

x^2-6*x-27 = 0

x^2-6*x-27 = 0

DELTA = (-6)^2-(-27*1*4)

DELTA = 144

DELTA > 0

x = (144^(1/2)+6)/(1*2) or x = (6-144^(1/2))/(1*2)

x = 9 or x = -3

(x+3)*(x-9) = 0

(x^2-81)/(x*(x-9)) = 0

1*x^2 = 81 // : 1

x^2 = 81

x^2 = 81 // ^ 1/2

abs(x) = 9

x = 9 or x = -9

x in { 9} 

x = -9

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