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

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


D( x )

x+2 = 0

x = 0

x+2 = 0

x+2 = 0

x+2 = 0 // - 2

x = -2

x = 0

x = 0

x in (-oo:-2) U (-2:0) U (0:+oo)

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

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

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

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

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

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

6-2*x^2-4*x = 0

6-2*x^2-4*x = 0

2*(3-x^2-2*x) = 0

3-x^2-2*x = 0

DELTA = (-2)^2-(-1*3*4)

DELTA = 16

DELTA > 0

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

x = -3 or x = 1

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

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

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

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

( x+3 )

x+3 = 0 // - 3

x = -3

( x-1 )

x-1 = 0 // + 1

x = 1

x in { -3, 1 }

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