4/x+4/(x-15)=1

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Solution for 4/x+4/(x-15)=1 equation: 


D( x )

x-15 = 0

x = 0

x-15 = 0

x-15 = 0

x-15 = 0 // + 15

x = 15

x = 0

x = 0

x in (-oo:0) U (0:15) U (15:+oo)

4/(x-15)+4/x = 1 // - 1

4/(x-15)+4/x-1 = 0

(4*x)/(x*(x-15))+(4*(x-15))/(x*(x-15))+(-1*x*(x-15))/(x*(x-15)) = 0

4*(x-15)-1*x*(x-15)+4*x = 0

8*x-x^2+15*x-60 = 0

23*x-x^2-60 = 0

23*x-x^2-60 = 0

23*x-x^2-60 = 0

DELTA = 23^2-(-60*(-1)*4)

DELTA = 289

DELTA > 0

x = (289^(1/2)-23)/(-1*2) or x = (-289^(1/2)-23)/(-1*2)

x = 3 or x = 20

(x-3)*(x-20) = 0

((x-3)*(x-20))/(x*(x-15)) = 0

((x-3)*(x-20))/(x*(x-15)) = 0 // * x*(x-15)

(x-3)*(x-20) = 0

( x-20 )

x-20 = 0 // + 20

x = 20

( x-3 )

x-3 = 0 // + 3

x = 3

x in { 20, 3 }

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