(4t-18)/(t-5)=2t/(t+3)

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Solution for (4t-18)/(t-5)=2t/(t+3) equation: 


D( t )

t-5 = 0

t+3 = 0

t-5 = 0

t-5 = 0

t-5 = 0 // + 5

t = 5

t+3 = 0

t+3 = 0

t+3 = 0 // - 3

t = -3

t in (-oo:-3) U (-3:5) U (5:+oo)

(4*t-18)/(t-5) = (2*t)/(t+3) // - (2*t)/(t+3)

(4*t-18)/(t-5)-((2*t)/(t+3)) = 0

(4*t-18)/(t-5)-2*t*(t+3)^-1 = 0

(4*t-18)/(t-5)+(-2*t)/(t+3) = 0

((4*t-18)*(t+3))/((t-5)*(t+3))+(-2*t*(t-5))/((t-5)*(t+3)) = 0

(4*t-18)*(t+3)-2*t*(t-5) = 0

2*t^2+4*t-54 = 0

2*t^2+4*t-54 = 0

2*(t^2+2*t-27) = 0

t^2+2*t-27 = 0

DELTA = 2^2-(-27*1*4)

DELTA = 112

DELTA > 0

t = (112^(1/2)-2)/(1*2) or t = (-112^(1/2)-2)/(1*2)

t = (4*7^(1/2)-2)/2 or t = (-4*7^(1/2)-2)/2

2*(t-((-4*7^(1/2)-2)/2))*(t-((4*7^(1/2)-2)/2)) = 0

(2*(t-((-4*7^(1/2)-2)/2))*(t-((4*7^(1/2)-2)/2)))/((t-5)*(t+3)) = 0

(2*(t-((-4*7^(1/2)-2)/2))*(t-((4*7^(1/2)-2)/2)))/((t-5)*(t+3)) = 0 // * (t-5)*(t+3)

2*(t-((-4*7^(1/2)-2)/2))*(t-((4*7^(1/2)-2)/2)) = 0

( t-((-4*7^(1/2)-2)/2) )

t-((-4*7^(1/2)-2)/2) = 0 // + (-4*7^(1/2)-2)/2

t = (-4*7^(1/2)-2)/2

( t-((4*7^(1/2)-2)/2) )

t-((4*7^(1/2)-2)/2) = 0 // + (4*7^(1/2)-2)/2

t = (4*7^(1/2)-2)/2

t in { (-4*7^(1/2)-2)/2, (4*7^(1/2)-2)/2 }

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