(3/(m+2))+(2/m)=(4m-4)/(m^2-4)

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Solution for (3/(m+2))+(2/m)=(4m-4)/(m^2-4) equation:


D( m )

m^2-4 = 0

m = 0

m+2 = 0

m^2-4 = 0

m^2-4 = 0

1*m^2 = 4 // : 1

m^2 = 4

m^2 = 4 // ^ 1/2

abs(m) = 2

m = 2 or m = -2

m = 0

m = 0

m+2 = 0

m+2 = 0

m+2 = 0 // - 2

m = -2

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

3/(m+2)+2/m = (4*m-4)/(m^2-4) // - (4*m-4)/(m^2-4)

3/(m+2)-((4*m-4)/(m^2-4))+2/m = 0

3/(m+2)+(-1*(4*m-4))/(m^2-4)+2/m = 0

(3*m*(m^2-4))/(m*(m+2)*(m^2-4))+(-1*m*(4*m-4)*(m+2))/(m*(m+2)*(m^2-4))+(2*(m+2)*(m^2-4))/(m*(m+2)*(m^2-4)) = 0

3*m*(m^2-4)-1*m*(4*m-4)*(m+2)+2*(m+2)*(m^2-4) = 0

2*m^3-m^3-4*m^2+4*m^2-4*m-8*m-16 = 0

m^3-12*m-16 = 0

m^3-12*m-16 = 0

m^3-12*m-16 = 0

{ 1, -1, 2, -2, 4, -4, 8, -8, 16, -16 }

1

m = 1

m^3-12*m-16 = -27

1

-1

m = -1

m^3-12*m-16 = -5

-1

2

m = 2

m^3-12*m-16 = -32

2

-2

m = -2

m^3-12*m-16 = 0

-2

m+2

m^2-2*m-8

m^3-12*m-16

m+2

-m^3-2*m^2

-2*m^2-12*m-16

2*m^2+4*m

-8*m-16

8*m+16

0

m^2-2*m-8 = 0

DELTA = (-2)^2-(-8*1*4)

DELTA = 36

DELTA > 0

m = (36^(1/2)+2)/(1*2) or m = (2-36^(1/2))/(1*2)

m = 4 or m = -2

m in { -2, 4, -2}

(m+2)^2*(m-4) = 0

((m+2)^2*(m-4))/(m*(m+2)*(m^2-4)) = 0

((m+2)^2*(m-4))/(m*(m+2)*(m^2-4)) = 0 // * m*(m+2)*(m^2-4)

(m+2)^2*(m-4) = 0

( m+2 )

m+2 = 0 // - 2

m = -2

( m-4 )

m-4 = 0 // + 4

m = 4

m in { -2}

m = 4

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