(1/(x-3))+(1/(x+1))=6/5

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Solution for (1/(x-3))+(1/(x+1))=6/5 equation:


D( x )

x-3 = 0

x+1 = 0

x-3 = 0

x-3 = 0

x-3 = 0 // + 3

x = 3

x+1 = 0

x+1 = 0

x+1 = 0 // - 1

x = -1

x in (-oo:-1) U (-1:3) U (3:+oo)

1/(x-3)+1/(x+1) = 6/5 // - 6/5

1/(x-3)+1/(x+1)-(6/5) = 0

1/(x-3)+1/(x+1)-6/5 = 0

(1*5*(x+1))/(5*(x-3)*(x+1))+(1*5*(x-3))/(5*(x-3)*(x+1))+(-6*(x-3)*(x+1))/(5*(x-3)*(x+1)) = 0

1*5*(x+1)+1*5*(x-3)-6*(x-3)*(x+1) = 0

10*x-6*x^2+12*x-10+18 = 0

22*x-6*x^2+8 = 0

22*x-6*x^2+8 = 0

2*(11*x-3*x^2+4) = 0

11*x-3*x^2+4 = 0

DELTA = 11^2-(-3*4*4)

DELTA = 169

DELTA > 0

x = (169^(1/2)-11)/(-3*2) or x = (-169^(1/2)-11)/(-3*2)

x = -1/3 or x = 4

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

(2*(x+1/3)*(x-4))/(5*(x-3)*(x+1)) = 0

(2*(x+1/3)*(x-4))/(5*(x-3)*(x+1)) = 0 // * 5*(x-3)*(x+1)

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

( x+1/3 )

x+1/3 = 0 // - 1/3

x = -1/3

( x-4 )

x-4 = 0 // + 4

x = 4

x in { -1/3, 4 }

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