(u+4)/(u^2+3u)-u/(u+3)=1

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Solution for (u+4)/(u^2+3u)-u/(u+3)=1 equation: 


D( u )

u^2+3*u = 0

u+3 = 0

u^2+3*u = 0

u^2+3*u = 0

u^2+3*u = 0

DELTA = 3^2-(0*1*4)

DELTA = 9

DELTA > 0

u = (9^(1/2)-3)/(1*2) or u = (-9^(1/2)-3)/(1*2)

u = 0 or u = -3

u+3 = 0

u+3 = 0

u+3 = 0 // - 3

u = -3

u in (-oo:-3) U (-3:0) U (0:+oo)

(u+4)/(u^2+3*u)-(u/(u+3)) = 1 // - 1

(u+4)/(u^2+3*u)-(u/(u+3))-1 = 0

(u+4)/(u^2+3*u)+(-1*u)/(u+3)-1 = 0

u^2+3*u = 0

u^2+3*u = 0

u*(u+3) = 0

u+3 = 0 // - 3

u = -3

u*(u+3) = 0

(u+4)/(u*(u+3))+(-1*u)/(u+3)-1 = 0

(u+4)/(u*(u+3))+(-1*u^2)/(u*(u+3))+(-1*u*(u+3))/(u*(u+3)) = 0

u-1*u*(u+3)-1*u^2+4 = 0

u-u^2-u^2-3*u+4 = 0

4-2*u^2-2*u = 0

4-2*u^2-2*u = 0

2*(2-u^2-u) = 0

2-u^2-u = 0

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

DELTA = 9

DELTA > 0

u = (9^(1/2)+1)/(-1*2) or u = (1-9^(1/2))/(-1*2)

u = -2 or u = 1

2*(u+2)*(u-1) = 0

(2*(u+2)*(u-1))/(u*(u+3)) = 0

(2*(u+2)*(u-1))/(u*(u+3)) = 0 // * u*(u+3)

2*(u+2)*(u-1) = 0

( u+2 )

u+2 = 0 // - 2

u = -2

( u-1 )

u-1 = 0 // + 1

u = 1

u in { -2, 1 }

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