6-(1/(x+1))=4/(x+2)

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Solution for 6-(1/(x+1))=4/(x+2) equation: 


D( x )

x+2 = 0

x+1 = 0

x+2 = 0

x+2 = 0

x+2 = 0 // - 2

x = -2

x+1 = 0

x+1 = 0

x+1 = 0 // - 1

x = -1

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

6-(1/(x+1)) = 4/(x+2) // - 4/(x+2)

6-(1/(x+1))-(4/(x+2)) = 0

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

6-1/(x+1)-4/(x+2) = 0

(-1*(x+2))/((x+1)*(x+2))+(-4*(x+1))/((x+1)*(x+2))+(6*(x+1)*(x+2))/((x+1)*(x+2)) = 0

6*(x+1)*(x+2)-1*(x+2)-4*(x+1) = 0

6*x^2-5*x+18*x-6+12 = 0

6*x^2+13*x+6 = 0

6*x^2+13*x+6 = 0

6*x^2+13*x+6 = 0

DELTA = 13^2-(4*6*6)

DELTA = 25

DELTA > 0

x = (25^(1/2)-13)/(2*6) or x = (-25^(1/2)-13)/(2*6)

x = -2/3 or x = -3/2

(x+3/2)*(x+2/3) = 0

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

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

(x+3/2)*(x+2/3) = 0

( x+2/3 )

x+2/3 = 0 // - 2/3

x = -2/3

( x+3/2 )

x+3/2 = 0 // - 3/2

x = -3/2

x in { -2/3, -3/2 }

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