5/(r-9)=8/r+5

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Solution for 5/(r-9)=8/r+5 equation: 


D( r )

r = 0

r-9 = 0

r = 0

r = 0

r-9 = 0

r-9 = 0

r-9 = 0 // + 9

r = 9

r in (-oo:0) U (0:9) U (9:+oo)

5/(r-9) = 8/r+5 // - 8/r+5

5/(r-9)-(8/r)-5 = 0

5/(r-9)-8*r^-1-5 = 0

5/(r-9)-8/r-5 = 0

(5*r)/(r*(r-9))+(-8*(r-9))/(r*(r-9))+(-5*r*(r-9))/(r*(r-9)) = 0

5*r-8*(r-9)-5*r*(r-9) = 0

45*r-5*r^2-3*r+72 = 0

42*r-5*r^2+72 = 0

42*r-5*r^2+72 = 0

42*r-5*r^2+72 = 0

DELTA = 42^2-(-5*4*72)

DELTA = 3204

DELTA > 0

r = (3204^(1/2)-42)/(-5*2) or r = (-3204^(1/2)-42)/(-5*2)

r = (6*89^(1/2)-42)/(-10) or r = (-6*89^(1/2)-42)/(-10)

(r-((6*89^(1/2)-42)/(-10)))*(r-((-6*89^(1/2)-42)/(-10))) = 0

((r-((6*89^(1/2)-42)/(-10)))*(r-((-6*89^(1/2)-42)/(-10))))/(r*(r-9)) = 0

((r-((6*89^(1/2)-42)/(-10)))*(r-((-6*89^(1/2)-42)/(-10))))/(r*(r-9)) = 0 // * r*(r-9)

(r-((6*89^(1/2)-42)/(-10)))*(r-((-6*89^(1/2)-42)/(-10))) = 0

( r-((-6*89^(1/2)-42)/(-10)) )

r-((-6*89^(1/2)-42)/(-10)) = 0 // + (-6*89^(1/2)-42)/(-10)

r = (-6*89^(1/2)-42)/(-10)

( r-((6*89^(1/2)-42)/(-10)) )

r-((6*89^(1/2)-42)/(-10)) = 0 // + (6*89^(1/2)-42)/(-10)

r = (6*89^(1/2)-42)/(-10)

r in { (-6*89^(1/2)-42)/(-10), (6*89^(1/2)-42)/(-10) }

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