(1/(36-6x)/(6-x))-1/(x-3)

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Solution for (1/(36-6x)/(6-x))-1/(x-3) equation: 


D( x )

6-x = 0

36-(6*x) = 0

x-3 = 0

6-x = 0

6-x = 0

6-x = 0 // - 6

-x = -6 // * -1

x = 6

36-(6*x) = 0

36-(6*x) = 0

36-6*x = 0

36-6*x = 0 // - 36

-6*x = -36 // : -6

x = -36/(-6)

x = 6

x-3 = 0

x-3 = 0

x-3 = 0 // + 3

x = 3

x in (-oo:3) U (3:6) U (6:+oo)

(1/(36-(6*x)))/(6-x)-(1/(x-3)) = 0

(1/(36-6*x))/(6-x)-(x-3)^-1 = 0

1/((36-6*x)*(6-x))-1/(x-3) = 0

(1*(x-3))/((36-6*x)*(6-x)*(x-3))+(-1*(36-6*x)*(6-x))/((36-6*x)*(6-x)*(x-3)) = 0

1*(x-3)-1*(36-6*x)*(6-x) = 0

73*x-6*x^2-219 = 0

73*x-6*x^2-219 = 0

73*x-6*x^2-219 = 0

DELTA = 73^2-(-219*(-6)*4)

DELTA = 73

DELTA > 0

x = (73^(1/2)-73)/(-6*2) or x = (-73^(1/2)-73)/(-6*2)

x = (73^(1/2)-73)/(-12) or x = (73^(1/2)+73)/12

(x-((73^(1/2)-73)/(-12)))*(x-((73^(1/2)+73)/12)) = 0

((x-((73^(1/2)-73)/(-12)))*(x-((73^(1/2)+73)/12)))/((36-6*x)*(6-x)*(x-3)) = 0

((x-((73^(1/2)-73)/(-12)))*(x-((73^(1/2)+73)/12)))/((36-6*x)*(6-x)*(x-3)) = 0 // * (36-6*x)*(6-x)*(x-3)

(x-((73^(1/2)-73)/(-12)))*(x-((73^(1/2)+73)/12)) = 0

( x-((73^(1/2)+73)/12) )

x-((73^(1/2)+73)/12) = 0 // + (73^(1/2)+73)/12

x = (73^(1/2)+73)/12

( x-((73^(1/2)-73)/(-12)) )

x-((73^(1/2)-73)/(-12)) = 0 // + (73^(1/2)-73)/(-12)

x = (73^(1/2)-73)/(-12)

x in { (73^(1/2)+73)/12, (73^(1/2)-73)/(-12) }

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