5/(x-2)+3/(x+8)=18/(x+8)(x-2)

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Solution for 5/(x-2)+3/(x+8)=18/(x+8)(x-2) equation: 


D( x )

x-2 = 0

x+8 = 0

x-2 = 0

x-2 = 0

x-2 = 0 // + 2

x = 2

x+8 = 0

x+8 = 0

x+8 = 0 // - 8

x = -8

x in (-oo:-8) U (-8:2) U (2:+oo)

5/(x-2)+3/(x+8) = (18/(x+8))*(x-2) // - (18/(x+8))*(x-2)

5/(x-2)+3/(x+8)-((18/(x+8))*(x-2)) = 0

5/(x-2)+3/(x+8)-18*(x-2)*(x+8)^-1 = 0

5/(x-2)+3/(x+8)+(-18*(x-2))/(x+8) = 0

(5*(x+8))/((x-2)*(x+8))+(3*(x-2))/((x-2)*(x+8))+(-18*(x-2)^2)/((x-2)*(x+8)) = 0

5*(x+8)+3*(x-2)-18*(x-2)^2 = 0

8*x-18*x^2+72*x-72+34 = 0

80*x-18*x^2-38 = 0

80*x-18*x^2-38 = 0

2*(40*x-9*x^2-19) = 0

40*x-9*x^2-19 = 0

DELTA = 40^2-(-19*(-9)*4)

DELTA = 916

DELTA > 0

x = (916^(1/2)-40)/(-9*2) or x = (-916^(1/2)-40)/(-9*2)

x = (2*229^(1/2)-40)/(-18) or x = (-2*229^(1/2)-40)/(-18)

2*(x-((2*229^(1/2)-40)/(-18)))*(x-((-2*229^(1/2)-40)/(-18))) = 0

(2*(x-((2*229^(1/2)-40)/(-18)))*(x-((-2*229^(1/2)-40)/(-18))))/((x-2)*(x+8)) = 0

(2*(x-((2*229^(1/2)-40)/(-18)))*(x-((-2*229^(1/2)-40)/(-18))))/((x-2)*(x+8)) = 0 // * (x-2)*(x+8)

2*(x-((2*229^(1/2)-40)/(-18)))*(x-((-2*229^(1/2)-40)/(-18))) = 0

( x-((-2*229^(1/2)-40)/(-18)) )

x-((-2*229^(1/2)-40)/(-18)) = 0 // + (-2*229^(1/2)-40)/(-18)

x = (-2*229^(1/2)-40)/(-18)

( x-((2*229^(1/2)-40)/(-18)) )

x-((2*229^(1/2)-40)/(-18)) = 0 // + (2*229^(1/2)-40)/(-18)

x = (2*229^(1/2)-40)/(-18)

x in { (-2*229^(1/2)-40)/(-18), (2*229^(1/2)-40)/(-18) }

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