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

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


D( x )

x+3 = 0

x^2-9 = 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 in (-oo:-3) U (-3:3) U (3:+oo)

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

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

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

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

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

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

6*x^2+3*x-6*x-45-18 = 0

6*x^2-3*x-63 = 0

6*x^2-3*x-63 = 0

3*(2*x^2-x-21) = 0

2*x^2-x-21 = 0

DELTA = (-1)^2-(-21*2*4)

DELTA = 169

DELTA > 0

x = (169^(1/2)+1)/(2*2) or x = (1-169^(1/2))/(2*2)

x = 7/2 or x = -3

3*(x+3)*(x-7/2) = 0

(3*(x+3)*(x-7/2))/((x^2-9)*(x+3)) = 0

(3*(x+3)*(x-7/2))/((x^2-9)*(x+3)) = 0 // * (x^2-9)*(x+3)

3*(x+3)*(x-7/2) = 0

( x+3 )

x+3 = 0 // - 3

x = -3

( x-7/2 )

x-7/2 = 0 // + 7/2

x = 7/2

x in { -3} 

x = 7/2

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