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

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


D( x )

3-x = 0

x+3 = 0

3-x = 0

3-x = 0

3-x = 0 // - 3

-x = -3 // * -1

x = 3

x+3 = 0

x+3 = 0

x+3 = 0 // - 3

x = -3

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

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

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

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

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

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

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

6*x^2+3*x-36*x+21+54 = 0

6*x^2-33*x+75 = 0

6*x^2-33*x+75 = 0

3*(2*x^2-11*x+25) = 0

2*x^2-11*x+25 = 0

DELTA = (-11)^2-(2*4*25)

DELTA = -79

DELTA < 0

3 = 0

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

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

3 = 0

x belongs to the empty set

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