(6/(5-t))+(3/(5-t))+(3/(25-t^2))=0

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Solution for (6/(5-t))+(3/(5-t))+(3/(25-t^2))=0 equation: 


D( t )

25-t^2 = 0

5-t = 0

25-t^2 = 0

25-t^2 = 0

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

t^2 = 25

t^2 = 25 // ^ 1/2

abs(t) = 5

t = 5 or t = -5

5-t = 0

5-t = 0

5-t = 0 // - 5

-t = -5 // * -1

t = 5

t in (-oo:-5) U (-5:5) U (5:+oo)

6/(5-t)+3/(5-t)+3/(25-t^2) = 0

(6*(25-t^2))/((5-t)*(25-t^2))+(3*(25-t^2))/((5-t)*(25-t^2))+(3*(5-t))/((5-t)*(25-t^2)) = 0

6*(25-t^2)+3*(25-t^2)+3*(5-t) = 0

15-9*t^2-3*t+225 = 0

240-9*t^2-3*t = 0

240-9*t^2-3*t = 0

3*(80-3*t^2-t) = 0

80-3*t^2-t = 0

DELTA = (-1)^2-(-3*4*80)

DELTA = 961

DELTA > 0

t = (961^(1/2)+1)/(-3*2) or t = (1-961^(1/2))/(-3*2)

t = -16/3 or t = 5

3*(t+16/3)*(t-5) = 0

(3*(t+16/3)*(t-5))/((5-t)*(25-t^2)) = 0

(3*(t+16/3)*(t-5))/((5-t)*(25-t^2)) = 0 // * (5-t)*(25-t^2)

3*(t+16/3)*(t-5) = 0

( t+16/3 )

t+16/3 = 0 // - 16/3

t = -16/3

( t-5 )

t-5 = 0 // + 5

t = 5

t in { 5} 

t = -16/3

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