((x+7)/(x+6))+1=(1/x+6)

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Solution for ((x+7)/(x+6))+1=(1/x+6) equation: 


D( x )

x = 0

x+6 = 0

x = 0

x = 0

x+6 = 0

x+6 = 0

x+6 = 0 // - 6

x = -6

x in (-oo:-6) U (-6:0) U (0:+oo)

(x+7)/(x+6)+1 = 1/x+6 // - 1/x+6

(x+7)/(x+6)-(1/x)-6+1 = 0

(x+7)/(x+6)-x^-1-6+1 = 0

(x+7)/(x+6)-1/x-6+1 = 0

(x*(x+7))/(x*(x+6))+(-1*(x+6))/(x*(x+6))+(-6*x*(x+6))/(x*(x+6))+(1*x*(x+6))/(x*(x+6)) = 0

x*(x+7)-1*(x+6)-6*x*(x+6)+1*x*(x+6) = 0

x^2-6*x^2+x^2+6*x-36*x+6*x-6 = 0

x^2-5*x^2-30*x+6*x-6 = 0

-4*x^2-24*x-6 = 0

-4*x^2-24*x-6 = 0

-2*(2*x^2+12*x+3) = 0

2*x^2+12*x+3 = 0

DELTA = 12^2-(2*3*4)

DELTA = 120

DELTA > 0

x = (120^(1/2)-12)/(2*2) or x = (-120^(1/2)-12)/(2*2)

x = (2*30^(1/2)-12)/4 or x = (-2*30^(1/2)-12)/4

-2*(x-((-2*30^(1/2)-12)/4))*(x-((2*30^(1/2)-12)/4)) = 0

(-2*(x-((-2*30^(1/2)-12)/4))*(x-((2*30^(1/2)-12)/4)))/(x*(x+6)) = 0

(-2*(x-((-2*30^(1/2)-12)/4))*(x-((2*30^(1/2)-12)/4)))/(x*(x+6)) = 0 // * x*(x+6)

-2*(x-((-2*30^(1/2)-12)/4))*(x-((2*30^(1/2)-12)/4)) = 0

( x-((-2*30^(1/2)-12)/4) )

x-((-2*30^(1/2)-12)/4) = 0 // + (-2*30^(1/2)-12)/4

x = (-2*30^(1/2)-12)/4

( x-((2*30^(1/2)-12)/4) )

x-((2*30^(1/2)-12)/4) = 0 // + (2*30^(1/2)-12)/4

x = (2*30^(1/2)-12)/4

x in { (-2*30^(1/2)-12)/4, (2*30^(1/2)-12)/4 }

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