(x+7)/(x+3)=((x-3)/(x-1))+1

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Solution for (x+7)/(x+3)=((x-3)/(x-1))+1 equation: 


D( x )

x+3 = 0

x-1 = 0

x+3 = 0

x+3 = 0

x+3 = 0 // - 3

x = -3

x-1 = 0

x-1 = 0

x-1 = 0 // + 1

x = 1

x in (-oo:-3) U (-3:1) U (1:+oo)

(x+7)/(x+3) = (x-3)/(x-1)+1 // - (x-3)/(x-1)+1

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

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

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

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

6*x-x^2-2*x+2+3 = 0

4*x-x^2+5 = 0

4*x-x^2+5 = 0

4*x-x^2+5 = 0

DELTA = 4^2-(-1*4*5)

DELTA = 36

DELTA > 0

x = (36^(1/2)-4)/(-1*2) or x = (-36^(1/2)-4)/(-1*2)

x = -1 or x = 5

(x+1)*(x-5) = 0

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

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

(x+1)*(x-5) = 0

( x+1 )

x+1 = 0 // - 1

x = -1

( x-5 )

x-5 = 0 // + 5

x = 5

x in { -1, 5 }

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