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

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Solution for 3/(x-1)-4/(x+2)=2 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:-2) U (-2:1) U (1:+oo)

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

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

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

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

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

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

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

14-2*x^2-3*x = 0

14-2*x^2-3*x = 0

14-2*x^2-3*x = 0

DELTA = (-3)^2-(-2*4*14)

DELTA = 121

DELTA > 0

x = (121^(1/2)+3)/(-2*2) or x = (3-121^(1/2))/(-2*2)

x = -7/2 or x = 2

(x+7/2)*(x-2) = 0

((x+7/2)*(x-2))/((x-1)*(x+2)) = 0

((x+7/2)*(x-2))/((x-1)*(x+2)) = 0 // * (x-1)*(x+2)

(x+7/2)*(x-2) = 0

( x+7/2 )

x+7/2 = 0 // - 7/2

x = -7/2

( x-2 )

x-2 = 0 // + 2

x = 2

x in { -7/2, 2 }

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