((x+6)/(x+7))+1=(x-4)/(x-1)

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Solution for ((x+6)/(x+7))+1=(x-4)/(x-1) equation: 


D( x )

x+7 = 0

x-1 = 0

x+7 = 0

x+7 = 0

x+7 = 0 // - 7

x = -7

x-1 = 0

x-1 = 0

x-1 = 0 // + 1

x = 1

x in (-oo:-7) U (-7:1) U (1:+oo)

(x+6)/(x+7)+1 = (x-4)/(x-1) // - (x-4)/(x-1)

(x+6)/(x+7)-((x-4)/(x-1))+1 = 0

(x+6)/(x+7)+(-1*(x-4))/(x-1)+1 = 0

((x+6)*(x-1))/((x+7)*(x-1))+(-1*(x-4)*(x+7))/((x+7)*(x-1))+(1*(x+7)*(x-1))/((x+7)*(x-1)) = 0

(x+6)*(x-1)-1*(x-4)*(x+7)+1*(x+7)*(x-1) = 0

x^2+2*x+6*x-7+22 = 0

x^2+8*x+15 = 0

x^2+8*x+15 = 0

x^2+8*x+15 = 0

DELTA = 8^2-(1*4*15)

DELTA = 4

DELTA > 0

x = (4^(1/2)-8)/(1*2) or x = (-4^(1/2)-8)/(1*2)

x = -3 or x = -5

(x+5)*(x+3) = 0

((x+5)*(x+3))/((x+7)*(x-1)) = 0

((x+5)*(x+3))/((x+7)*(x-1)) = 0 // * (x+7)*(x-1)

(x+5)*(x+3) = 0

( x+3 )

x+3 = 0 // - 3

x = -3

( x+5 )

x+5 = 0 // - 5

x = -5

x in { -3, -5 }

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