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

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

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

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

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

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

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

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

x^2+x-3*x-5+2 = 0

x^2-2*x-3 = 0

x^2-2*x-3 = 0

x^2-2*x-3 = 0

DELTA = (-2)^2-(-3*1*4)

DELTA = 16

DELTA > 0

x = (16^(1/2)+2)/(1*2) or x = (2-16^(1/2))/(1*2)

x = 3 or x = -1

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

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

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

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

( x+1 )

x+1 = 0 // - 1

x = -1

( x-3 )

x-3 = 0 // + 3

x = 3

x in { -1, 3 }

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