(2x)/(x-3)+5/(x-1)=1

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Solution for (2x)/(x-3)+5/(x-1)=1 equation: 


D( x )

x-3 = 0

x-1 = 0

x-3 = 0

x-3 = 0

x-3 = 0 // + 3

x = 3

x-1 = 0

x-1 = 0

x-1 = 0 // + 1

x = 1

x in (-oo:1) U (1:3) U (3:+oo)

(2*x)/(x-3)+5/(x-1) = 1 // - 1

(2*x)/(x-3)+5/(x-1)-1 = 0

(2*x*(x-1))/((x-3)*(x-1))+(5*(x-3))/((x-3)*(x-1))+(-1*(x-3)*(x-1))/((x-3)*(x-1)) = 0

2*x*(x-1)+5*(x-3)-1*(x-3)*(x-1) = 0

2*x^2-x^2+3*x+4*x-15-3 = 0

x^2+7*x-18 = 0

x^2+7*x-18 = 0

x^2+7*x-18 = 0

DELTA = 7^2-(-18*1*4)

DELTA = 121

DELTA > 0

x = (121^(1/2)-7)/(1*2) or x = (-121^(1/2)-7)/(1*2)

x = 2 or x = -9

(x+9)*(x-2) = 0

((x+9)*(x-2))/((x-3)*(x-1)) = 0

((x+9)*(x-2))/((x-3)*(x-1)) = 0 // * (x-3)*(x-1)

(x+9)*(x-2) = 0

( x+9 )

x+9 = 0 // - 9

x = -9

( x-2 )

x-2 = 0 // + 2

x = 2

x in { -9, 2 }

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