6/(c-3)=(c+3)/(c^2-9)-5

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Solution for 6/(c-3)=(c+3)/(c^2-9)-5 equation:


D( c )

c^2-9 = 0

c-3 = 0

c^2-9 = 0

c^2-9 = 0

1*c^2 = 9 // : 1

c^2 = 9

c^2 = 9 // ^ 1/2

abs(c) = 3

c = 3 or c = -3

c-3 = 0

c-3 = 0

c-3 = 0 // + 3

c = 3

c in (-oo:-3) U (-3:3) U (3:+oo)

6/(c-3) = (c+3)/(c^2-9)-5 // - (c+3)/(c^2-9)-5

6/(c-3)-((c+3)/(c^2-9))+5 = 0

6/(c-3)+(-1*(c+3))/(c^2-9)+5 = 0

(6*(c^2-9))/((c-3)*(c^2-9))+(-1*(c+3)*(c-3))/((c-3)*(c^2-9))+(5*(c-3)*(c^2-9))/((c-3)*(c^2-9)) = 0

6*(c^2-9)-1*(c+3)*(c-3)+5*(c-3)*(c^2-9) = 0

5*c^3+5*c^2-15*c^2-45*c-45+135 = 0

5*c^3-10*c^2-45*c+90 = 0

5*c^3-10*c^2-45*c+90 = 0

5*(c^3-2*c^2-9*c+18) = 0

c^3-2*c^2-9*c+18 = 0

{ 1, -1, 2, -2, 3, -3, 6, -6, 9, -9, 18, -18 }

1

c = 1

c^3-2*c^2-9*c+18 = 8

1

-1

c = -1

c^3-2*c^2-9*c+18 = 24

-1

2

c = 2

c^3-2*c^2-9*c+18 = 0

2

c-2

c^2-9

c^3-2*c^2-9*c+18

c-2

2*c^2-c^3

18-9*c

9*c-18

0

c^2-9 = 0

DELTA = 0^2-(-9*1*4)

DELTA = 36

DELTA > 0

c = (36^(1/2)+0)/(1*2) or c = (0-36^(1/2))/(1*2)

c = 3 or c = -3

c in { -3, 3, 2}

5*(c+3)*(c-3)*(c-2) = 0

(5*(c+3)*(c-3)*(c-2))/((c-3)*(c^2-9)) = 0

(5*(c+3)*(c-3)*(c-2))/((c-3)*(c^2-9)) = 0 // * (c-3)*(c^2-9)

5*(c+3)*(c-3)*(c-2) = 0

( c+3 )

c+3 = 0 // - 3

c = -3

( c-2 )

c-2 = 0 // + 2

c = 2

( c-3 )

c-3 = 0 // + 3

c = 3

c in { -3}

c in { 3}

c = 2

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