(15/x)-5+7=25/(x-5)

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Solution for (15/x)-5+7=25/(x-5) 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)

15/x-5+7 = 25/(x-5) // - 25/(x-5)

15/x-(25/(x-5))-5+7 = 0

15/x-25*(x-5)^-1-5+7 = 0

15/x-25/(x-5)-5+7 = 0

(-25*x)/(x*(x-5))+(15*(x-5))/(x*(x-5))+(-5*x*(x-5))/(x*(x-5))+(7*x*(x-5))/(x*(x-5)) = 0

15*(x-5)-5*x*(x-5)+7*x*(x-5)-25*x = 0

7*x^2-5*x^2-10*x+25*x-35*x-75 = 0

7*x^2-5*x^2+15*x-35*x-75 = 0

2*x^2-20*x-75 = 0

2*x^2-20*x-75 = 0

2*x^2-20*x-75 = 0

DELTA = (-20)^2-(-75*2*4)

DELTA = 1000

DELTA > 0

x = (1000^(1/2)+20)/(2*2) or x = (20-1000^(1/2))/(2*2)

x = (10*10^(1/2)+20)/4 or x = (20-10*10^(1/2))/4

(x-((20-10*10^(1/2))/4))*(x-((10*10^(1/2)+20)/4)) = 0

((x-((20-10*10^(1/2))/4))*(x-((10*10^(1/2)+20)/4)))/(x*(x-5)) = 0

((x-((20-10*10^(1/2))/4))*(x-((10*10^(1/2)+20)/4)))/(x*(x-5)) = 0 // * x*(x-5)

(x-((20-10*10^(1/2))/4))*(x-((10*10^(1/2)+20)/4)) = 0

( x-((10*10^(1/2)+20)/4) )

x-((10*10^(1/2)+20)/4) = 0 // + (10*10^(1/2)+20)/4

x = (10*10^(1/2)+20)/4

( x-((20-10*10^(1/2))/4) )

x-((20-10*10^(1/2))/4) = 0 // + (20-10*10^(1/2))/4

x = (20-10*10^(1/2))/4

x in { (10*10^(1/2)+20)/4, (20-10*10^(1/2))/4 }

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