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

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


D( x )

x-2 = 0

x-1 = 0

x-2 = 0

x-2 = 0

x-2 = 0 // + 2

x = 2

x-1 = 0

x-1 = 0

x-1 = 0 // + 1

x = 1

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

2-((x-3)/(x-2)) > (x-5)/(x-1) // - (x-5)/(x-1)

2-((x-3)/(x-2))-((x-5)/(x-1)) > 0

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

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

2*(x-2)*(x-1)-1*(x-3)*(x-1)-1*(x-5)*(x-2) > 0

2*x^2-2*x^2+11*x-6*x-13+4 > 0

5*x-9 > 0

(5*x-9)/((x-2)*(x-1)) > 0

(5*x-9)/((x-2)*(x-1)) > 0 // * ((x-2)*(x-1))^2

(5*x-9)*(x-2)*(x-1) > 0

( 5*x-9 )

5*x-9 > 0 // + 9

5*x > 9 // : 5

x > 9/5

( x-1 )

x-1 > 0 // + 1

x > 1

( x-2 )

x-2 > 0 // + 2

x > 2

	(-oo:1)	(1:9/5)	(9/5:2)	(2:+oo)
5*x-9	-	-	+	+
x-1	-	+	+	+
x-2	-	-	-	+


x in (1:9/5) U (2:+oo)

(1:9/5) U (2:+oo)

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