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

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


D( x )

x = 0

x-1 = 0

x = 0

x = 0

x-1 = 0

x-1 = 0

x-1 = 0 // + 1

x = 1

x in (-oo:0) U (0:1) U (1:+oo)

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

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

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

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

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

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

x-x^2-x+4 >= 0

4-x^2 >= 0

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

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

x*(4-x^2)*(x-1) >= 0

( 4-x^2 )

-1*x^2 >= -4

-1*x^2 >= -4 // * -1

1*x^2 <= 4

1*x^2 <= 4 // : 1

x^2 <= 4/1

x^2 <= 4

x^2 <= 4 // ^ 1/2

abs(x) <= 2

x in <-2:2>

( x-1 )

x-1 >= 0 // + 1

x >= 1

( x )

x+0 >= 0 // - 0

x >= 0

(-oo:-2) (-2:0) (0:1) (1:2) (2:+oo) 4-x^2 - + + + - x-1 - - - + + x - - + + +

x in <-2:0) U (1:2>

<-2:0) U (1:2>

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