3+x/(9-x^2)

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


D( x )

9-x^2 = 0

9-x^2 = 0

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

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

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

x-3*x^2+27 = 0

x-3*x^2+27 = 0

x-3*x^2+27 = 0

DELTA = 1^2-(-3*4*27)

DELTA = 325

DELTA > 0

x = (325^(1/2)-1)/(-3*2) or x = (-325^(1/2)-1)/(-3*2)

x = (5*13^(1/2)-1)/(-6) or x = (-5*13^(1/2)-1)/(-6)

(x-((5*13^(1/2)-1)/(-6)))*(x-((-5*13^(1/2)-1)/(-6))) = 0

((x-((5*13^(1/2)-1)/(-6)))*(x-((-5*13^(1/2)-1)/(-6))))/(9-x^2) = 0

((x-((5*13^(1/2)-1)/(-6)))*(x-((-5*13^(1/2)-1)/(-6))))/(9-x^2) = 0 // * 9-x^2

(x-((5*13^(1/2)-1)/(-6)))*(x-((-5*13^(1/2)-1)/(-6))) = 0

( x-((-5*13^(1/2)-1)/(-6)) )

x-((-5*13^(1/2)-1)/(-6)) = 0 // + (-5*13^(1/2)-1)/(-6)

x = (-5*13^(1/2)-1)/(-6)

( x-((5*13^(1/2)-1)/(-6)) )

x-((5*13^(1/2)-1)/(-6)) = 0 // + (5*13^(1/2)-1)/(-6)

x = (5*13^(1/2)-1)/(-6)

x in { (-5*13^(1/2)-1)/(-6), (5*13^(1/2)-1)/(-6) }

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