5/x+3+1/x-2=8/(x+3)(x-2)

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Solution for 5/x+3+1/x-2=8/(x+3)(x-2) equation:


D( x )

x = 0

x+3 = 0

x = 0

x = 0

x+3 = 0

x+3 = 0

x+3 = 0 // - 3

x = -3

x in (-oo:-3) U (-3:0) U (0:+oo)

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

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

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

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

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

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

3*x^2-8*x^2-2*x^2+21*x+x-6*x+9*x+3+15 = 0

3*x^2-8*x^2-2*x^2+22*x-6*x+9*x+18 = 0

3*x^2-10*x^2+16*x+9*x+18 = 0

25*x-7*x^2+18 = 0

25*x-7*x^2+18 = 0

25*x-7*x^2+18 = 0

DELTA = 25^2-(-7*4*18)

DELTA = 1129

DELTA > 0

x = (1129^(1/2)-25)/(-7*2) or x = (-1129^(1/2)-25)/(-7*2)

x = (1129^(1/2)-25)/(-14) or x = (1129^(1/2)+25)/14

(x-((1129^(1/2)-25)/(-14)))*(x-((1129^(1/2)+25)/14)) = 0

((x-((1129^(1/2)-25)/(-14)))*(x-((1129^(1/2)+25)/14)))/(x*(x+3)) = 0

((x-((1129^(1/2)-25)/(-14)))*(x-((1129^(1/2)+25)/14)))/(x*(x+3)) = 0 // * x*(x+3)

(x-((1129^(1/2)-25)/(-14)))*(x-((1129^(1/2)+25)/14)) = 0

( x-((1129^(1/2)+25)/14) )

x-((1129^(1/2)+25)/14) = 0 // + (1129^(1/2)+25)/14

x = (1129^(1/2)+25)/14

( x-((1129^(1/2)-25)/(-14)) )

x-((1129^(1/2)-25)/(-14)) = 0 // + (1129^(1/2)-25)/(-14)

x = (1129^(1/2)-25)/(-14)

x in { (1129^(1/2)+25)/14, (1129^(1/2)-25)/(-14) }

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