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

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


D( x )

x+2 = 0

(x+1)*(X+2) = 0

x+2 = 0

x+2 = 0

x+2 = 0 // - 2

x = -2

(x+1)*(X+2) = 0

(x+1)*(X+2) = 0

x+1 = 0 // - 1

x = -1

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

-1/((x+1)*(X+2)) = 1/(x+2)+3 // - 1/(x+2)+3

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

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

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

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

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

-(X*x)-X-3*X*x^2-9*X*x-6*X-6*x^2-3*x-18*x-12-4 = 0

-3*X*x^2-10*X*x-7*X-6*x^2-21*x-16 = 0

(-3*X*x^2-10*X*x-7*X-6*x^2-21*x-16)/((x+1)*(X+2)*(x+2)) = 0

(-3*X*x^2-10*X*x-7*X-6*x^2-21*x-16)/((x+1)*(X+2)*(x+2)) = 0 // * (x+1)*(X+2)*(x+2)

-3*X*x^2-10*X*x-7*X-6*x^2-21*x-16 = 0

-7*X-6*x^2-21*x-16 = 0

DELTA = (-21)^2-(-6*4*(-7*X-16))

DELTA = 24*(-7*X-16)+441

24*(-7*X-16)+441 = 0

24*(-7*X-16)+441 = 0

57-168*X = 0

57-168*X = 0

57-168*X = 0 // - 57

-168*X = -57 // : -168

X = -57/(-168)

X = 19/56

DELTA = 0 <=> t_3 = 19/56

x = 21/(-6*2) i X = 19/56

x = -7/4 i X = 19/56

( x = ((24*(-7*X-16)+441)^(1/2)+21)/(-6*2) or x = (21-(24*(-7*X-16)+441)^(1/2))/(-6*2) ) i X > 19/56

( x = ((24*(-7*X-16)+441)^(1/2)+21)/(-12) or x = (21-(24*(-7*X-16)+441)^(1/2))/(-12) ) i X > 19/56

X-19/56 > 0

X-19/56 > 0 // + 19/56

X > 19/56

x in { -7/4, ((24*(-7*X-16)+441)^(1/2)+21)/(-12), (21-(24*(-7*X-16)+441)^(1/2))/(-12) }

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