(5p-5/p)/(9p-9/4p^2)

Solution for (5p-5/p)/(9p-9/4p^2) equation:

D( p )

p = 0

9*p-((9/4)*p^2) = 0

p = 0

p = 0

9*p-((9/4)*p^2) = 0

9*p-((9/4)*p^2) = 0

(-9/4)*p^2+9*p = 0

9*p-9/4*p^2 = 0

DELTA = 9^2-(-9/4*0*4)

DELTA = 81

DELTA > 0

p = (81^(1/2)-9)/(-9/4*2) or p = (-81^(1/2)-9)/(-9/4*2)

p = 0 or p = 4

p in (-oo:0) U (0:4) U (4:+oo)

(5*p-(5/p))/(9*p-((9/4)*p^2)) = 0

(5*p-5*p^-1)/((-9/4)*p^2+9*p) = 0

(5*p-5*p^-1)/(9*p-9/4*p^2) = 0

5*p-5*p^-1 = 0

5*p^-1*(p^2-1) = 0

1*p^2 = 1 // : 1

p^2 = 1

p^2 = 1 // ^ 1/2

abs(p) = 1

p = 1 or p = -1

5*p^-1*(p-1)*(p+1) = 0

9*p-9/4*p^2 = 0

9*p*(1-1/4*p) = 0

1-1/4*p = 0 // - 1

-1/4*p = -1 // : -1/4

p = -1/(-1/4)

p = 4

9*p*(p-4) = 0

(5*p^-1*(p-1)*(p+1))/(9*p*(p-4)) = 0

( 5*p^-1 )

5*p^-1 = 0 // : 5

p^-1 = 0

p należy do O

( p+1 )

p+1 = 0 // - 1

p = -1

( p-1 )

p-1 = 0 // + 1

p = 1

p in { -1, 1 }