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

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


D( x )

x-2 = 0

x-2 = 0

x-2 = 0

x-2 = 0 // + 2

x = 2

x in (-oo:2) U (2:+oo)

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

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

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

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

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

4*X-x^2+5*x-10 = 0

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

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

4*X-x^2+5*x-10 = 0

4*X-x^2+5*x-10 = 0

DELTA = 5^2-(-1*4*(4*X-10))

DELTA = 4*(4*X-10)+25

4*(4*X-10)+25 = 0

4*(4*X-10)+25 = 0

16*X-15 = 0

16*X-15 = 0

16*X-15 = 0 // + 15

16*X = 15 // : 16

X = 15/16

DELTA = 0  <=>  t_3 = 15/16

x = -5/(-1*2) i X = 15/16

x = 5/2 i X = 15/16

( x = ((4*(4*X-10)+25)^(1/2)-5)/(-1*2) or x = (-(4*(4*X-10)+25)^(1/2)-5)/(-1*2) ) i X > 15/16

( x = ((4*(4*X-10)+25)^(1/2)-5)/(-2) or x = ((4*(4*X-10)+25)^(1/2)+5)/2 ) i X > 15/16

X-(15/16) > 0

X-15/16 > 0

X-15/16 > 0 // + 15/16

X > 15/16

x in { 5/2, ((4*(4*X-10)+25)^(1/2)-5)/(-2), ((4*(4*X-10)+25)^(1/2)+5)/2 }

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