y=3/x-5/x^2

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Solution for y=3/x-5/x^2 equation: 


D( x )

x = 0

x^2 = 0

x = 0

x = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

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

y = 3/x-(5/(x^2)) // - 3/x-(5/(x^2))

5/(x^2)-(3/x)+y = 0

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

5*x^-2-3*x^-1+y = 0

t_1 = x^-1

5*t_1^2-3*t_1^1+y = 0

5*t_1^2-3*t_1+y = 0

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

DELTA = 9-20*y

9-20*y = 0

9-20*y = 0 // - 9

-20*y = -9 // : -20

y = -9/(-20)

y = 9/20

DELTA = 0  <=>  t_2 = 9/20

t_1 = 3/(2*5) i y = 9/20

t_1 = 3/10 i y = 9/20

( t_1 = ((9-20*y)^(1/2)+3)/(2*5) or t_1 = (3-(9-20*y)^(1/2))/(2*5) ) i y > 9/20

( t_1 = ((9-20*y)^(1/2)+3)/10 or t_1 = (3-(9-20*y)^(1/2))/10 ) i y > 9/20

y-9/20 > 0

y-9/20 > 0 // + 9/20

y > 9/20

t_1 = 3/10

x^-1-3/10 = 0

1*x^-1 = 3/10 // : 1

x^-1 = 3/10

-1 < 0

1/(x^1) = 3/10 // * x^1

1 = 3/10*x^1 // : 3/10

10/3 = x^1

x = 10/3

t_1 = ((9-20*y)^(1/2)+3)/10

t_3 = -(((9-20*y)^(1/2)+3)/10)

t_3+x^-1 = 0

1*x^-1 = -t_3 // : 1

x^-1 = -t_3

-1 < 0

1/(x^1) = -t_3 // * x^1

1 = -t_3*x^1 // : -t_3

-t_3^-1 = x^1

x = t_3^-1

t_1 = (3-(9-20*y)^(1/2))/10

t_4 = -((3-(9-20*y)^(1/2))/10)

t_4+x^-1 = 0

1*x^-1 = -t_4 // : 1

x^-1 = -t_4

-1 < 0

1/(x^1) = -t_4 // * x^1

1 = -t_4*x^1 // : -t_4

-t_4^-1 = x^1

x = t_4^-1

x in { 10/3, (-(((9-20*y)^(1/2)+3)/10))^-1, (-((3-(9-20*y)^(1/2))/10))^-1 }

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