((8t^2-35t+12)/(8t^2+61t-24))/((32t^2-36t+9)/(4t^2+29t-24))

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Solution for ((8t^2-35t+12)/(8t^2+61t-24))/((32t^2-36t+9)/(4t^2+29t-24)) equation: 


D( t )

4*t^2+29*t-24 = 0

(32*t^2-(36*t)+9)/(4*t^2+29*t-24) = 0

8*t^2+61*t-24 = 0

4*t^2+29*t-24 = 0

4*t^2+29*t-24 = 0

4*t^2+29*t-24 = 0

DELTA = 29^2-(-24*4*4)

DELTA = 1225

DELTA > 0

t = (1225^(1/2)-29)/(2*4) or t = (-1225^(1/2)-29)/(2*4)

t = 3/4 or t = -8

(32*t^2-(36*t)+9)/(4*t^2+29*t-24) = 0

(32*t^2-(36*t)+9)/(4*t^2+29*t-24) = 0

(32*t^2-36*t+9)/(4*t^2+29*t-24) = 0

32*t^2-36*t+9 = 0

32*t^2-36*t+9 = 0

DELTA = (-36)^2-(4*9*32)

DELTA = 144

DELTA > 0

t = (144^(1/2)+36)/(2*32) or t = (36-144^(1/2))/(2*32)

t = 3/4 or t = 3/8

(t-3/8)*(t-3/4) = 0

4*t^2+29*t-24 = 0

4*t^2+29*t-24 = 0

DELTA = 29^2-(-24*4*4)

DELTA = 1225

DELTA > 0

t = (1225^(1/2)-29)/(2*4) or t = (-1225^(1/2)-29)/(2*4)

t = 3/4 or t = -8

(t+8)*(t-3/4) = 0

((t-3/8)*(t-3/4))/((t+8)*(t-3/4)) = 0

( t-3/4 )

t-3/4 = 0 // + 3/4

t = 3/4

( t-3/8 )

t-3/8 = 0 // + 3/8

t = 3/8

8*t^2+61*t-24 = 0

8*t^2+61*t-24 = 0

8*t^2+61*t-24 = 0

DELTA = 61^2-(-24*4*8)

DELTA = 4489

DELTA > 0

t = (4489^(1/2)-61)/(2*8) or t = (-4489^(1/2)-61)/(2*8)

t = 3/8 or t = -8

t in (-oo:-8) U (-8:3/8) U (3/8:3/4) U (3/4:+oo)

((8*t^2-(35*t)+12)/(8*t^2+61*t-24))/((32*t^2-(36*t)+9)/(4*t^2+29*t-24)) = 0

((8*t^2-35*t+12)/(8*t^2+61*t-24))/((32*t^2-36*t+9)/(4*t^2+29*t-24)) = 0

((8*t^2-35*t+12)*(4*t^2+29*t-24))/((8*t^2+61*t-24)*(32*t^2-36*t+9)) = 0

8*t^2-35*t+12 = 0

8*t^2-35*t+12 = 0

DELTA = (-35)^2-(4*8*12)

DELTA = 841

DELTA > 0

t = (841^(1/2)+35)/(2*8) or t = (35-841^(1/2))/(2*8)

t = 4 or t = 3/8

(t-3/8)*(t-4) = 0

8*t^2+61*t-24 = 0

8*t^2+61*t-24 = 0

DELTA = 61^2-(-24*4*8)

DELTA = 4489

DELTA > 0

t = (4489^(1/2)-61)/(2*8) or t = (-4489^(1/2)-61)/(2*8)

t = 3/8 or t = -8

(t+8)*(t-3/8) = 0

32*t^2-36*t+9 = 0

32*t^2-36*t+9 = 0

DELTA = (-36)^2-(4*9*32)

DELTA = 144

DELTA > 0

t = (144^(1/2)+36)/(2*32) or t = (36-144^(1/2))/(2*32)

t = 3/4 or t = 3/8

(t-3/8)*(t-3/4) = 0

4*t^2+29*t-24 = 0

4*t^2+29*t-24 = 0

DELTA = 29^2-(-24*4*4)

DELTA = 1225

DELTA > 0

t = (1225^(1/2)-29)/(2*4) or t = (-1225^(1/2)-29)/(2*4)

t = 3/4 or t = -8

(t+8)*(t-3/4) = 0

((t-3/8)*(t-4)*(t+8)*(t-3/4))/((t+8)*(t-3/8)^2*(t-3/4)) = 0

( t+8 )

t+8 = 0 // - 8

t = -8

( t-3/4 )

t-3/4 = 0 // + 3/4

t = 3/4

( t-3/8 )

t-3/8 = 0 // + 3/8

t = 3/8

( t-4 )

t-4 = 0 // + 4

t = 4

t in { -8} 

t in { 3/4} 

t in { 3/8} 

t = 4

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