(((((5+y)^2-20y)/(25-5y))-(5/(y-5))^-2)^2)/((25y^2-y^4)/625)

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Solution for (((((5+y)^2-20y)/(25-5y))-(5/(y-5))^-2)^2)/((25y^2-y^4)/625) equation: 


D( y )

25-(5*y) = 0

y-5 = 0

(25*y^2-y^4)/625 = 0

5/(y-5) = 0

25-(5*y) = 0

25-(5*y) = 0

25-5*y = 0

25-5*y = 0 // - 25

-5*y = -25 // : -5

y = -25/(-5)

y = 5

y-5 = 0

y-5 = 0

y-5 = 0 // + 5

y = 5

(25*y^2-y^4)/625 = 0

(25*y^2-y^4)/625 = 0

25*y^2-y^4 = 0

y^2*(25-y^2) = 0

-1*y^2 = -25 // : -1

y^2 = 25

y^2 = 25 // ^ 1/2

abs(y) = 5

y = 5 or y = -5

y^2*(y-5)*(y+5) = 0

(y^2*(y-5)*(y+5))/625 = 0

( y+5 )

y+5 = 0 // - 5

y = -5

( y-5 )

y-5 = 0 // + 5

y = 5

( y^2 )

1*y^2 = 0 // : 1

y^2 = 0

y = 0

5/(y-5) = 0

5/(y-5) = 0

y in (-oo:-5) U (-5:0) U (0:5) U (5:+oo)

((((y+5)^2-(20*y))/(25-(5*y))-(5/(y-5))^-2)^2)/((25*y^2-y^4)/625) = 0

((((y+5)^2-20*y)/(25-5*y)-(5/(y-5))^-2)^2)/((25*y^2-y^4)/625) = 0

(625*(((y+5)^2-20*y)/(25-5*y)+(-1*(y-5)^2)/(5^2))^2)/(25*y^2-y^4) = 0

25*y^2-y^4 = 0

y^2*(25-y^2) = 0

-1*y^2 = -25 // : -1

y^2 = 25

y^2 = 25 // ^ 1/2

abs(y) = 5

y = 5 or y = -5

y^2*(y-5)*(y+5) = 0

((y+5)^2-20*y)/(25-5*y)+(-1*(y-5)^2)/(5^2) = 0

(5^2*((y+5)^2-20*y))/(5^2*(25-5*y))+(-1*(y-5)^2*(25-5*y))/(5^2*(25-5*y)) = 0

5^2*((y+5)^2-20*y)-1*(y-5)^2*(25-5*y) = 0

5*y^3-50*y^2+125*y = 0

5*y^3-50*y^2+125*y = 0

5*y*(y^2-10*y+25) = 0

y^2-10*y+25 = 0

DELTA = (-10)^2-(1*4*25)

DELTA = 0

y = 10/(1*2)

y = 5 or y = 5

5*y*(y-5)^2 = 0

(5*y*(y-5)^2)/(5^2*(25-5*y)) = 0

(5*y*(y-5)^2)/(5^2*(25-5*y)) = 0 // * 5^2*(25-5*y)

5*y*(y-5)^2 = 0

(625*(5*y)^2*(y-5)^4)/(y^2*(y-5)*(y+5)) = 0

( 5*y )

5*y = 0 // : 5

y = 0

( y-5 )

y-5 = 0 // + 5

y = 5

y in { 0} 

y in { 5} 

y belongs to the empty set

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