(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) = 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

6*t^2-16*t-54 = 0

6*t^2-16*t-54 = 0

2*(3*t^2-8*t-27) = 0

3*t^2-8*t-27 = 0

DELTA = (-8)^2-(-27*3*4)

DELTA = 388

DELTA > 0

t = (388^(1/2)+8)/(2*3) or t = (8-388^(1/2))/(2*3)

t = (2*97^(1/2)+8)/6 or t = (8-2*97^(1/2))/6

2*(t-((8-2*97^(1/2))/6))*(t-((2*97^(1/2)+8)/6)) = 0

(2*(t-((8-2*97^(1/2))/6))*(t-((2*97^(1/2)+8)/6)))/((t-5)*(t+3)) = 0

(2*(t-((8-2*97^(1/2))/6))*(t-((2*97^(1/2)+8)/6)))/((t-5)*(t+3)) = 0 // * (t-5)*(t+3)

2*(t-((8-2*97^(1/2))/6))*(t-((2*97^(1/2)+8)/6)) = 0

( t-((2*97^(1/2)+8)/6) )

t-((2*97^(1/2)+8)/6) = 0 // + (2*97^(1/2)+8)/6

t = (2*97^(1/2)+8)/6

( t-((8-2*97^(1/2))/6) )

t-((8-2*97^(1/2))/6) = 0 // + (8-2*97^(1/2))/6

t = (8-2*97^(1/2))/6

t in { (2*97^(1/2)+8)/6, (8-2*97^(1/2))/6 }

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