7=(r^3-1)/(r-1)

Solution for 7=(r^3-1)/(r-1) equation:

D( r )

r-1 = 0

r-1 = 0

r-1 = 0

r-1 = 0 // + 1

r = 1

r in (-oo:1) U (1:+oo)

7 = (r^3-1)/(r-1) // - (r^3-1)/(r-1)

7-((r^3-1)/(r-1)) = 0

(-1*(r^3-1))/(r-1)+7 = 0

(-1*(r^3-1))/(r-1)+(7*(r-1))/(r-1) = 0

7*(r-1)-1*(r^3-1) = 0

7*r-r^3-6 = 0

7*r-r^3-6 = 0

7*r-r^3-6 = 0

{ 1, -1, 2, -2, 3, -3, 6, -6 }

1

r = 1

7*r-r^3-6 = 0

1

r-1

6-r^2-r

7*r-r^3-6

r-1

r^3-r^2

7*r-r^2-6

r^2-r

6*r-6

6-6*r

0

6-r^2-r = 0

DELTA = (-1)^2-(-1*4*6)

DELTA = 25

DELTA > 0

r = (25^(1/2)+1)/(-1*2) or r = (1-25^(1/2))/(-1*2)

r = -3 or r = 2

r in { -3, 2, 1} 

(r+3)*(r-2)*(r-1) = 0

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

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

(r+3)*(r-2)*(r-1) = 0

( r+3 )

r+3 = 0 // - 3

r = -3

( r-1 )

r-1 = 0 // + 1

r = 1

( r-2 )

r-2 = 0 // + 2

r = 2

r in { 1} 

r in { -3, 2 }