(t-2)/(2t-8)=5/(4t-16)

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Solution for (t-2)/(2t-8)=5/(4t-16) equation:


D( t )

4*t-16 = 0

2*t-8 = 0

4*t-16 = 0

4*t-16 = 0

4*t-16 = 0 // + 16

4*t = 16 // : 4

t = 16/4

t = 4

2*t-8 = 0

2*t-8 = 0

2*t-8 = 0 // + 8

2*t = 8 // : 2

t = 8/2

t = 4

t in (-oo:4) U (4:+oo)

(t-2)/(2*t-8) = 5/(4*t-16) // - 5/(4*t-16)

(t-2)/(2*t-8)-(5/(4*t-16)) = 0

(t-2)/(2*t-8)-5*(4*t-16)^-1 = 0

(t-2)/(2*t-8)-5/(4*t-16) = 0

((t-2)*(4*t-16))/((2*t-8)*(4*t-16))+(-5*(2*t-8))/((2*t-8)*(4*t-16)) = 0

(t-2)*(4*t-16)-5*(2*t-8) = 0

4*t^2-34*t+72 = 0

4*t^2-34*t+72 = 0

2*(2*t^2-17*t+36) = 0

2*t^2-17*t+36 = 0

DELTA = (-17)^2-(2*4*36)

DELTA = 1

DELTA > 0

t = (1^(1/2)+17)/(2*2) or t = (17-1^(1/2))/(2*2)

t = 9/2 or t = 4

2*(t-4)*(t-9/2) = 0

(2*(t-4)*(t-9/2))/((2*t-8)*(4*t-16)) = 0

(2*(t-4)*(t-9/2))/((2*t-8)*(4*t-16)) = 0 // * (2*t-8)*(4*t-16)

2*(t-4)*(t-9/2) = 0

( 2 )

2 = 0

t belongs to the empty set

( t-4 )

t-4 = 0 // + 4

t = 4

( t-9/2 )

t-9/2 = 0 // + 9/2

t = 9/2

t in { 4}

t = 9/2

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