-5+((6)/(x+5))=((1)/((x+5)^2))

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Solution for -5+((6)/(x+5))=((1)/((x+5)^2)) equation: 


D( x )

x+5 = 0

(x+5)^2 = 0

x+5 = 0

x+5 = 0

x+5 = 0 // - 5

x = -5

(x+5)^2 = 0

(x+5)^2 = 0

x+5 = 0 // - 5

x = -5

x in (-oo:-5) U (-5:+oo)

6/(x+5)-5 = 1/((x+5)^2) // - 1/((x+5)^2)

6/(x+5)-(1/((x+5)^2))-5 = 0

6/(x+5)-(x+5)^-2-5 = 0

6/(x+5)-1/((x+5)^2)-5 = 0

(6*(x+5))/((x+5)^2)-1/((x+5)^2)+(-5*(x+5)^2)/((x+5)^2) = 0

6*(x+5)-5*(x+5)^2-1 = 0

6*x-5*x^2-50*x-125+29 = 0

-5*x^2-44*x-96 = 0

-5*x^2-44*x-96 = 0

-1*(5*x^2+44*x+96) = 0

5*x^2+44*x+96 = 0

DELTA = 44^2-(4*5*96)

DELTA = 16

DELTA > 0

x = (16^(1/2)-44)/(2*5) or x = (-16^(1/2)-44)/(2*5)

x = -4 or x = -24/5

-1*(x+24/5)*(x+4) = 0

(-1*(x+24/5)*(x+4))/((x+5)^2) = 0

(-1*(x+24/5)*(x+4))/((x+5)^2) = 0 // * (x+5)^2

-1*(x+24/5)*(x+4) = 0

( x+24/5 )

x+24/5 = 0 // - 24/5

x = -24/5

( x+4 )

x+4 = 0 // - 4

x = -4

x in { -24/5, -4 }

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