1/(x-3)-3/(x-2)=4/(1-2x)

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Solution for 1/(x-3)-3/(x-2)=4/(1-2x) equation: 


D( x )

x-2 = 0

x-3 = 0

1-(2*x) = 0

x-2 = 0

x-2 = 0

x-2 = 0 // + 2

x = 2

x-3 = 0

x-3 = 0

x-3 = 0 // + 3

x = 3

1-(2*x) = 0

1-(2*x) = 0

1-2*x = 0

1-2*x = 0 // - 1

-2*x = -1 // : -2

x = -1/(-2)

x = 1/2

x in (-oo:1/2) U (1/2:2) U (2:3) U (3:+oo)

1/(x-3)-(3/(x-2)) = 4/(1-(2*x)) // - 4/(1-(2*x))

1/(x-3)-(3/(x-2))-(4/(1-(2*x))) = 0

1/(x-3)-3*(x-2)^-1-4*(1-2*x)^-1 = 0

1/(x-3)-3/(x-2)-4/(1-2*x) = 0

(1*(x-2)*(1-2*x))/((x-3)*(x-2)*(1-2*x))+(-3*(x-3)*(1-2*x))/((x-3)*(x-2)*(1-2*x))+(-4*(x-3)*(x-2))/((x-3)*(x-2)*(1-2*x)) = 0

1*(x-2)*(1-2*x)-3*(x-3)*(1-2*x)-4*(x-3)*(x-2) = 0

4*x^2-4*x^2-16*x+20*x-24+7 = 0

4*x-17 = 0

(4*x-17)/((x-3)*(x-2)*(1-2*x)) = 0

(4*x-17)/((x-3)*(x-2)*(1-2*x)) = 0 // * (x-3)*(x-2)*(1-2*x)

4*x-17 = 0

4*x-17 = 0 // + 17

4*x = 17 // : 4

x = 17/4

x = 17/4

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