4/(x+3)-6/(x-3)=10/(x^2-9)

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Solution for 4/(x+3)-6/(x-3)=10/(x^2-9) equation:


D( x )

x-3 = 0

x^2-9 = 0

x+3 = 0

x-3 = 0

x-3 = 0

x-3 = 0 // + 3

x = 3

x^2-9 = 0

x^2-9 = 0

1*x^2 = 9 // : 1

x^2 = 9

x^2 = 9 // ^ 1/2

abs(x) = 3

x = 3 or x = -3

x+3 = 0

x+3 = 0

x+3 = 0 // - 3

x = -3

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

4/(x+3)-(6/(x-3)) = 10/(x^2-9) // - 10/(x^2-9)

4/(x+3)-(6/(x-3))-(10/(x^2-9)) = 0

4/(x+3)-6*(x-3)^-1-10*(x^2-9)^-1 = 0

4/(x+3)-6/(x-3)-10/(x^2-9) = 0

(4*(x-3)*(x^2-9))/((x+3)*(x-3)*(x^2-9))+(-6*(x+3)*(x^2-9))/((x+3)*(x-3)*(x^2-9))+(-10*(x+3)*(x-3))/((x+3)*(x-3)*(x^2-9)) = 0

4*(x-3)*(x^2-9)-6*(x+3)*(x^2-9)-10*(x+3)*(x-3) = 0

18*x-2*x^3-30*x^2-10*x^2+90+270 = 0

18*x-2*x^3-40*x^2+360 = 0

18*x-2*x^3-40*x^2+360 = 0

2*(9*x-x^3-20*x^2+180) = 0

9*x-x^3-20*x^2+180

x*(9-x^2)-20*x^2+180

20*(9-x^2)+x*(9-x^2)

(x+20)*(9-x^2)

2*(x+20)*(9-x^2) = 0

(2*(x+20)*(9-x^2))/((x+3)*(x-3)*(x^2-9)) = 0

(2*(x+20)*(9-x^2))/((x+3)*(x-3)*(x^2-9)) = 0 // * (x+3)*(x-3)*(x^2-9)

2*(x+20)*(9-x^2) = 0

( 9-x^2 )

-1*x^2 = -9 // : -1

x^2 = 9

x^2 = 9 // ^ 1/2

abs(x) = 3

x = 3 or x = -3

( x+20 )

x+20 = 0 // - 20

x = -20

x in { 3}

x in { -3}

x = -20

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