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

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


D( x )

x+1 = 0

x+6 = 0

x+1 = 0

x+1 = 0

x+1 = 0 // - 1

x = -1

x+6 = 0

x+6 = 0

x+6 = 0 // - 6

x = -6

x in (-oo:-6) U (-6:-1) U (-1:+oo)

(-6/(x+1))*(x+6) = 6/(x+6)+5 // - 6/(x+6)+5

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

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

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

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

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

-6*x^2-5*x^2-78*x-35*x-222-30 = 0

-11*x^2-113*x-252 = 0

-11*x^2-113*x-252 = 0

-1*(11*x^2+113*x+252) = 0

11*x^2+113*x+252 = 0

DELTA = 113^2-(4*11*252)

DELTA = 1681

DELTA > 0

x = (1681^(1/2)-113)/(2*11) or x = (-1681^(1/2)-113)/(2*11)

x = -36/11 or x = -7

-1*(x+7)*(x+36/11) = 0

(-1*(x+7)*(x+36/11))/((x+1)*(x+6)) = 0

(-1*(x+7)*(x+36/11))/((x+1)*(x+6)) = 0 // * (x+1)*(x+6)

-1*(x+7)*(x+36/11) = 0

( x+36/11 )

x+36/11 = 0 // - 36/11

x = -36/11

( x+7 )

x+7 = 0 // - 7

x = -7

x in { -36/11, -7 }

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