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

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


D( x )

x^2+x = 0

x+1 = 0

x^2+x = 0

x^2+x = 0

x^2+x = 0

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

DELTA = 1

DELTA > 0

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

x = 0 or x = -1

x+1 = 0

x+1 = 0

x+1 = 0 // - 1

x = -1

x in (-oo:-1) U (-1:0) U (0:+oo)

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

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

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

4/(x+1)+4/(x^2+x)+1 = 0

x^2+x = 0

x^2+x = 0

x*(x+1) = 0

x+1 = 0 // - 1

x = -1

x*(x+1) = 0

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

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

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

x^2+4*x+x+4 = 0

x^2+5*x+4 = 0

x^2+5*x+4 = 0

x^2+5*x+4 = 0

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

DELTA = 9

DELTA > 0

x = (9^(1/2)-5)/(1*2) or x = (-9^(1/2)-5)/(1*2)

x = -1 or x = -4

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

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

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

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

( x+1 )

x+1 = 0 // - 1

x = -1

( x+4 )

x+4 = 0 // - 4

x = -4

x in { -1} 

x = -4

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