x=y/(x+4)

Solution for x=y/(x+4) equation:

D( x )

x+4 = 0

x+4 = 0

x+4 = 0

x+4 = 0 // - 4

x = -4

x in (-oo:-4) U (-4:+oo)

x = y/(x+4) // - y/(x+4)

x-(y/(x+4)) = 0

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

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

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

x^2+4*x-y = 0

(x^2+4*x-y)/(x+4) = 0

(x^2+4*x-y)/(x+4) = 0 // * x+4

x^2+4*x-y = 0

x^2+4*x-y = 0

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

DELTA = 4*y+16

4*y+16 = 0

4*y+16 = 0 // - 16

4*y = -16 // : 4

y = -16/4

y = -4

DELTA = 0  <=>  t_3 = -4

x = -4/(1*2) i y = -4

x = -2 i y = -4

( x = ((4*y+16)^(1/2)-4)/(1*2) or x = (-(4*y+16)^(1/2)-4)/(1*2) ) i y > -4

( x = ((4*y+16)^(1/2)-4)/2 or x = (-((4*y+16)^(1/2)+4))/2 ) i y > -4

y+4 > 0

y+4 > 0 // - 4

y > -4

x in { -2, ((4*y+16)^(1/2)-4)/2, (-((4*y+16)^(1/2)+4))/2 }