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 )

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

3-x = 0

x+3 = 0

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

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

( x+3 )

x+3 = 0 // - 3

x = -3

( x-3 )

x-3 = 0 // + 3

x = 3

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)^-1*(x+3)^-1 = 0

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

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

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

3*x^2+12*x+6*x-63-18 = 0

3*x^2+18*x-81 = 0

3*x^2+18*x-81 = 0

3*(x^2+6*x-27) = 0

x^2+6*x-27 = 0

DELTA = 6^2-(-27*1*4)

DELTA = 144

DELTA > 0

x = (144^(1/2)-6)/(1*2) or x = (-144^(1/2)-6)/(1*2)

x = 3 or x = -9

3*(x+9)*(x-3) = 0

(3*(x+9)*(x-3))/((x+3)*(3-x)*(x-3)) = 0

(3*(x+9)*(x-3))/((x+3)*(3-x)*(x-3)) = 0 // * (x+3)*(3-x)*(x-3)

3*(x+9)*(x-3) = 0

( x+9 )

x+9 = 0 // - 9

x = -9

( x-3 )

x-3 = 0 // + 3

x = 3

x in { 3}

x = -9

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