((x+7)/(x+3))=((x-2)/(x+1))+1

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Solution for ((x+7)/(x+3))=((x-2)/(x+1))+1 equation: 


D( x )

x+1 = 0

x+3 = 0

x+1 = 0

x+1 = 0

x+1 = 0 // - 1

x = -1

x+3 = 0

x+3 = 0

x+3 = 0 // - 3

x = -3

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

(x+7)/(x+3) = (x-2)/(x+1)+1 // - (x-2)/(x+1)+1

(x+7)/(x+3)-((x-2)/(x+1))-1 = 0

(x+7)/(x+3)+(-1*(x-2))/(x+1)-1 = 0

((x+7)*(x+1))/((x+3)*(x+1))+(-1*(x-2)*(x+3))/((x+3)*(x+1))+(-1*(x+3)*(x+1))/((x+3)*(x+1)) = 0

(x+7)*(x+1)-1*(x-2)*(x+3)-1*(x+3)*(x+1) = 0

7*x-x^2-4*x-3+13 = 0

3*x-x^2+10 = 0

3*x-x^2+10 = 0

3*x-x^2+10 = 0

DELTA = 3^2-(-1*4*10)

DELTA = 49

DELTA > 0

x = (49^(1/2)-3)/(-1*2) or x = (-49^(1/2)-3)/(-1*2)

x = -2 or x = 5

(x+2)*(x-5) = 0

((x+2)*(x-5))/((x+3)*(x+1)) = 0

((x+2)*(x-5))/((x+3)*(x+1)) = 0 // * (x+3)*(x+1)

(x+2)*(x-5) = 0

( x+2 )

x+2 = 0 // - 2

x = -2

( x-5 )

x-5 = 0 // + 5

x = 5

x in { -2, 5 }

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