2+1/u-7=5/(u-2)(u-7)

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Solution for 2+1/u-7=5/(u-2)(u-7) equation: 


D( u )

u = 0

u-2 = 0

u = 0

u = 0

u-2 = 0

u-2 = 0

u-2 = 0 // + 2

u = 2

u in (-oo:0) U (0:2) U (2:+oo)

1/u-7+2 = (5/(u-2))*(u-7) // - (5/(u-2))*(u-7)

1/u-((5/(u-2))*(u-7))-7+2 = 0

1/u-5*(u-7)*(u-2)^-1-7+2 = 0

(-5*(u-7))/(u-2)+1/u-7+2 = 0

(-5*u*(u-7))/(u*(u-2))+(1*(u-2))/(u*(u-2))+(-7*u*(u-2))/(u*(u-2))+(2*u*(u-2))/(u*(u-2)) = 0

1*(u-2)-5*u*(u-7)-7*u*(u-2)+2*u*(u-2) = 0

2*u^2-5*u^2-7*u^2+36*u+14*u-4*u-2 = 0

2*u^2-12*u^2+50*u-4*u-2 = 0

46*u-10*u^2-2 = 0

46*u-10*u^2-2 = 0

2*(23*u-5*u^2-1) = 0

23*u-5*u^2-1 = 0

DELTA = 23^2-(-5*(-1)*4)

DELTA = 509

DELTA > 0

u = (509^(1/2)-23)/(-5*2) or u = (-509^(1/2)-23)/(-5*2)

u = (509^(1/2)-23)/(-10) or u = (509^(1/2)+23)/10

2*(u-((509^(1/2)-23)/(-10)))*(u-((509^(1/2)+23)/10)) = 0

(2*(u-((509^(1/2)-23)/(-10)))*(u-((509^(1/2)+23)/10)))/(u*(u-2)) = 0

(2*(u-((509^(1/2)-23)/(-10)))*(u-((509^(1/2)+23)/10)))/(u*(u-2)) = 0 // * u*(u-2)

2*(u-((509^(1/2)-23)/(-10)))*(u-((509^(1/2)+23)/10)) = 0

( u-((509^(1/2)+23)/10) )

u-((509^(1/2)+23)/10) = 0 // + (509^(1/2)+23)/10

u = (509^(1/2)+23)/10

( u-((509^(1/2)-23)/(-10)) )

u-((509^(1/2)-23)/(-10)) = 0 // + (509^(1/2)-23)/(-10)

u = (509^(1/2)-23)/(-10)

u in { (509^(1/2)+23)/10, (509^(1/2)-23)/(-10) }

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