(x+6)/(x+2)=((x+5)/(x+7))+1

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Solution for (x+6)/(x+2)=((x+5)/(x+7))+1 equation: 


D( x )

x+7 = 0

x+2 = 0

x+7 = 0

x+7 = 0

x+7 = 0 // - 7

x = -7

x+2 = 0

x+2 = 0

x+2 = 0 // - 2

x = -2

x in (-oo:-7) U (-7:-2) U (-2:+oo)

(x+6)/(x+2) = (x+5)/(x+7)+1 // - (x+5)/(x+7)+1

(x+6)/(x+2)-((x+5)/(x+7))-1 = 0

(x+6)/(x+2)+(-1*(x+5))/(x+7)-1 = 0

((x+6)*(x+7))/((x+2)*(x+7))+(-1*(x+5)*(x+2))/((x+2)*(x+7))+(-1*(x+2)*(x+7))/((x+2)*(x+7)) = 0

(x+6)*(x+7)-1*(x+5)*(x+2)-1*(x+2)*(x+7) = 0

6*x-x^2-9*x-14+32 = 0

18-x^2-3*x = 0

18-x^2-3*x = 0

18-x^2-3*x = 0

DELTA = (-3)^2-(-1*4*18)

DELTA = 81

DELTA > 0

x = (81^(1/2)+3)/(-1*2) or x = (3-81^(1/2))/(-1*2)

x = -6 or x = 3

(x+6)*(x-3) = 0

((x+6)*(x-3))/((x+2)*(x+7)) = 0

((x+6)*(x-3))/((x+2)*(x+7)) = 0 // * (x+2)*(x+7)

(x+6)*(x-3) = 0

( x+6 )

x+6 = 0 // - 6

x = -6

( x-3 )

x-3 = 0 // + 3

x = 3

x in { -6, 3 }

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