((x)/(2x+4))-((x+4)/(x+1))=1

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Solution for ((x)/(2x+4))-((x+4)/(x+1))=1 equation:


D( x )

x+1 = 0

2*x+4 = 0

x+1 = 0

x+1 = 0

x+1 = 0 // - 1

x = -1

2*x+4 = 0

2*x+4 = 0

2*x+4 = 0 // - 4

2*x = -4 // : 2

x = -4/2

x = -2

x in (-oo:-2) U (-2:-1) U (-1:+oo)

x/(2*x+4)-((x+4)/(x+1)) = 1 // - 1

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

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

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

x*(x+1)-1*(x+4)*(2*x+4)-1*(2*x+4)*(x+1) = 0

-x^2-2*x^2-11*x-6*x-16-4 = 0

-3*x^2-17*x-20 = 0

-3*x^2-17*x-20 = 0

-1*(3*x^2+17*x+20) = 0

3*x^2+17*x+20 = 0

DELTA = 17^2-(3*4*20)

DELTA = 49

DELTA > 0

x = (49^(1/2)-17)/(2*3) or x = (-49^(1/2)-17)/(2*3)

x = -5/3 or x = -4

-1*(x+4)*(x+5/3) = 0

(-1*(x+4)*(x+5/3))/((2*x+4)*(x+1)) = 0

(-1*(x+4)*(x+5/3))/((2*x+4)*(x+1)) = 0 // * (2*x+4)*(x+1)

-1*(x+4)*(x+5/3) = 0

( x+4 )

x+4 = 0 // - 4

x = -4

( x+5/3 )

x+5/3 = 0 // - 5/3

x = -5/3

x in { -4, -5/3 }

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