(1/x-1)+(x/x+4)=5/(x+4)(x-1)

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Solution for (1/x-1)+(x/x+4)=5/(x+4)(x-1) equation: 


D( x )

x+4 = 0

x = 0

x+4 = 0

x+4 = 0

x+4 = 0 // - 4

x = -4

x = 0

x = 0

x in (-oo:-4) U (-4:0) U (0:+oo)

1/x+x/x-1+4 = (5/(x+4))*(x-1) // - (5/(x+4))*(x-1)

1/x-((5/(x+4))*(x-1))+x/x-1+4 = 0

1/x-5*(x-1)*(x+4)^-1+x/x-1+4 = 0

(-5*(x-1))/(x+4)+1/x-1+1+4 = 0

(-5*x*(x-1))/(x*(x+4))+(1*(x+4))/(x*(x+4))+(1*x*(x+4))/(x*(x+4))+(-1*x*(x+4))/(x*(x+4))+(4*x*(x+4))/(x*(x+4)) = 0

1*(x+4)-5*x*(x-1)+1*x*(x+4)-1*x*(x+4)+4*x*(x+4) = 0

x^2-5*x^2-x^2+4*x^2+6*x+4*x-4*x+16*x+4 = 0

4*x^2-4*x^2-x^2+10*x-4*x+16*x+4 = 0

4*x^2-5*x^2+6*x+16*x+4 = 0

22*x-x^2+4 = 0

22*x-x^2+4 = 0

22*x-x^2+4 = 0

DELTA = 22^2-(-1*4*4)

DELTA = 500

DELTA > 0

x = (500^(1/2)-22)/(-1*2) or x = (-500^(1/2)-22)/(-1*2)

x = (10*5^(1/2)-22)/(-2) or x = (-10*5^(1/2)-22)/(-2)

(x-((10*5^(1/2)-22)/(-2)))*(x-((-10*5^(1/2)-22)/(-2))) = 0

((x-((10*5^(1/2)-22)/(-2)))*(x-((-10*5^(1/2)-22)/(-2))))/(x*(x+4)) = 0

((x-((10*5^(1/2)-22)/(-2)))*(x-((-10*5^(1/2)-22)/(-2))))/(x*(x+4)) = 0 // * x*(x+4)

(x-((10*5^(1/2)-22)/(-2)))*(x-((-10*5^(1/2)-22)/(-2))) = 0

( x-((-10*5^(1/2)-22)/(-2)) )

x-((-10*5^(1/2)-22)/(-2)) = 0 // + (-10*5^(1/2)-22)/(-2)

x = (-10*5^(1/2)-22)/(-2)

( x-((10*5^(1/2)-22)/(-2)) )

x-((10*5^(1/2)-22)/(-2)) = 0 // + (10*5^(1/2)-22)/(-2)

x = (10*5^(1/2)-22)/(-2)

x in { (-10*5^(1/2)-22)/(-2), (10*5^(1/2)-22)/(-2) }

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