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

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


D( x )

3-x = 0

x-3 = 0

3-x = 0

3-x = 0

3-x = 0 // - 3

-x = -3 // * -1

x = 3

x-3 = 0

x-3 = 0

x-3 = 0 // + 3

x = 3

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

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

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

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

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

11*x-2*x^2-15 = 0

11*x-2*x^2-15 = 0

11*x-2*x^2-15 = 0

DELTA = 11^2-(-15*(-2)*4)

DELTA = 1

DELTA > 0

x = (1^(1/2)-11)/(-2*2) or x = (-1^(1/2)-11)/(-2*2)

x = 5/2 or x = 3

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

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

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

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

( x-3 )

x-3 = 0 // + 3

x = 3

( x-5/2 )

x-5/2 = 0 // + 5/2

x = 5/2

x in { 3} 

x = 5/2

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