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

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

7-2*x-4*x+20 = 0

27-6*x = 0

(27-6*x)/(x*(x-5)) = 0

(27-6*x)/(x*(x-5)) = 0 // * x*(x-5)

27-6*x = 0

27-6*x = 0 // - 27

-6*x = -27 // : -6

x = -27/(-6)

x = 9/2

x = 9/2

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