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

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


D( x )

x-1 = 0

x-1 = 0

x-1 = 0

x-1 = 0 // + 1

x = 1

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

(x-5)/(x-1) >= 3 // - 3

(x-5)/(x-1)-3 >= 0

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

x-3*(x-1)-5 >= 0

-2*x-2 >= 0

(-2*x-2)/(x-1) >= 0

(-2*x-2)/(x-1) >= 0 // * (x-1)^2

(-2*x-2)*(x-1) >= 0

( -2*x-2 )

-2*x-2 >= 0 // + 2

-2*x >= 2 // : -2

x <= 2/(-2)

x <= -1

( x-1 )

x-1 >= 0 // + 1

x >= 1

	(-oo:-1)	(-1:1)	(1:+oo)
-2*x-2	+	-	-
x-1	-	-	+


x in <-1:1)

<-1:1)

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