-5/(x+2)=-8+1/(x+1)

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Solution for -5/(x+2)=-8+1/(x+1) 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)

-5/(x+2) = 1/(x+1)-8 // - 1/(x+1)-8

8-5/(x+2)-(1/(x+1)) = 0

8-5/(x+2)-(x+1)^-1 = 0

8-5/(x+2)-1/(x+1) = 0

(-5*(x+1))/((x+2)*(x+1))+(-1*(x+2))/((x+2)*(x+1))+(8*(x+2)*(x+1))/((x+2)*(x+1)) = 0

8*(x+2)*(x+1)-5*(x+1)-1*(x+2) = 0

8*x^2-6*x+24*x-7+16 = 0

8*x^2+18*x+9 = 0

8*x^2+18*x+9 = 0

8*x^2+18*x+9 = 0

DELTA = 18^2-(4*8*9)

DELTA = 36

DELTA > 0

x = (36^(1/2)-18)/(2*8) or x = (-36^(1/2)-18)/(2*8)

x = -3/4 or x = -3/2

(x+3/2)*(x+3/4) = 0

((x+3/2)*(x+3/4))/((x+2)*(x+1)) = 0

((x+3/2)*(x+3/4))/((x+2)*(x+1)) = 0 // * (x+2)*(x+1)

(x+3/2)*(x+3/4) = 0

( x+3/2 )

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

x = -3/2

( x+3/4 )

x+3/4 = 0 // - 3/4

x = -3/4

x in { -3/2, -3/4 }

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