200/(x-5)-200/(x)=2

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Solution for 200/(x-5)-200/(x)=2 equation: 


D( x )

x-5 = 0

x = 0

x-5 = 0

x-5 = 0

x-5 = 0 // + 5

x = 5

x = 0

x = 0

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

200/(x-5)-(200/x) = 2 // - 2

200/(x-5)-(200/x)-2 = 0

200/(x-5)-200*x^-1-2 = 0

200/(x-5)-200/x-2 = 0

(200*x)/(x*(x-5))+(-200*(x-5))/(x*(x-5))+(-2*x*(x-5))/(x*(x-5)) = 0

200*x-200*(x-5)-2*x*(x-5) = 0

10*x-2*x^2+1000 = 0

10*x-2*x^2+1000 = 0

2*(5*x-x^2+500) = 0

5*x-x^2+500 = 0

DELTA = 5^2-(-1*4*500)

DELTA = 2025

DELTA > 0

x = (2025^(1/2)-5)/(-1*2) or x = (-2025^(1/2)-5)/(-1*2)

x = -20 or x = 25

2*(x+20)*(x-25) = 0

(2*(x+20)*(x-25))/(x*(x-5)) = 0

(2*(x+20)*(x-25))/(x*(x-5)) = 0 // * x*(x-5)

2*(x+20)*(x-25) = 0

( x+20 )

x+20 = 0 // - 20

x = -20

( x-25 )

x-25 = 0 // + 25

x = 25

x in { -20, 25 }

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