(1/(x-1))+(1/(x+2))=5/4

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Solution for (1/(x-1))+(1/(x+2))=5/4 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)

1/(x-1)+1/(x+2) = 5/4 // - 5/4

1/(x-1)+1/(x+2)-(5/4) = 0

1/(x-1)+1/(x+2)-5/4 = 0

(1*4*(x+2))/(4*(x-1)*(x+2))+(1*4*(x-1))/(4*(x-1)*(x+2))+(-5*(x-1)*(x+2))/(4*(x-1)*(x+2)) = 0

1*4*(x+2)+1*4*(x-1)-5*(x-1)*(x+2) = 0

8*x-5*x^2-5*x+4+10 = 0

3*x-5*x^2+14 = 0

3*x-5*x^2+14 = 0

3*x-5*x^2+14 = 0

DELTA = 3^2-(-5*4*14)

DELTA = 289

DELTA > 0

x = (289^(1/2)-3)/(-5*2) or x = (-289^(1/2)-3)/(-5*2)

x = -7/5 or x = 2

(x+7/5)*(x-2) = 0

((x+7/5)*(x-2))/(4*(x-1)*(x+2)) = 0

((x+7/5)*(x-2))/(4*(x-1)*(x+2)) = 0 // * 4*(x-1)*(x+2)

(x+7/5)*(x-2) = 0

( x+7/5 )

x+7/5 = 0 // - 7/5

x = -7/5

( x-2 )

x-2 = 0 // + 2

x = 2

x in { -7/5, 2 }

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