7/(x^2-5x)-2/(x+5)=(4/x)

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Solution for 7/(x^2-5x)-2/(x+5)=(4/x) equation: 


D( x )

x+5 = 0

x = 0

x^2-(5*x) = 0

x+5 = 0

x+5 = 0

x+5 = 0 // - 5

x = -5

x = 0

x = 0

x^2-(5*x) = 0

x^2-(5*x) = 0

x^2-5*x = 0

x^2-5*x = 0

DELTA = (-5)^2-(0*1*4)

DELTA = 25

DELTA > 0

x = (25^(1/2)+5)/(1*2) or x = (5-25^(1/2))/(1*2)

x = 5 or x = 0

x in (-oo:-5) U (-5:0) U (0:5) U (5:+oo)

7/(x^2-(5*x))-(2/(x+5)) = 4/x // - 4/x

7/(x^2-(5*x))-(2/(x+5))-(4/x) = 0

7/(x^2-5*x)-2*(x+5)^-1-4*x^-1 = 0

7/(x^2-5*x)-2/(x+5)-4/x = 0

x^2-5*x = 0

x^2-5*x = 0

x*(x-5) = 0

x-5 = 0 // + 5

x = 5

x*(x-5) = 0

7/(x*(x-5))-2/(x+5)-4/x = 0

(7*(x+5))/(x*(x-5)*(x+5))+(-2*x*(x-5))/(x*(x-5)*(x+5))+(-4*(x-5)*(x+5))/(x*(x-5)*(x+5)) = 0

7*(x+5)-2*x*(x-5)-4*(x-5)*(x+5) = 0

17*x-2*x^2-4*x^2+35+100 = 0

17*x-6*x^2+135 = 0

17*x-6*x^2+135 = 0

17*x-6*x^2+135 = 0

DELTA = 17^2-(-6*4*135)

DELTA = 3529

DELTA > 0

x = (3529^(1/2)-17)/(-6*2) or x = (-3529^(1/2)-17)/(-6*2)

x = (3529^(1/2)-17)/(-12) or x = (3529^(1/2)+17)/12

(x-((3529^(1/2)-17)/(-12)))*(x-((3529^(1/2)+17)/12)) = 0

((x-((3529^(1/2)-17)/(-12)))*(x-((3529^(1/2)+17)/12)))/(x*(x-5)*(x+5)) = 0

((x-((3529^(1/2)-17)/(-12)))*(x-((3529^(1/2)+17)/12)))/(x*(x-5)*(x+5)) = 0 // * x*(x-5)*(x+5)

(x-((3529^(1/2)-17)/(-12)))*(x-((3529^(1/2)+17)/12)) = 0

( x-((3529^(1/2)+17)/12) )

x-((3529^(1/2)+17)/12) = 0 // + (3529^(1/2)+17)/12

x = (3529^(1/2)+17)/12

( x-((3529^(1/2)-17)/(-12)) )

x-((3529^(1/2)-17)/(-12)) = 0 // + (3529^(1/2)-17)/(-12)

x = (3529^(1/2)-17)/(-12)

x in { (3529^(1/2)+17)/12, (3529^(1/2)-17)/(-12) }

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