(4/x+3)+(1/x-1)=9/(x+3)(x-1)

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Solution for (4/x+3)+(1/x-1)=9/(x+3)(x-1) equation:


D( x )

x = 0

x+3 = 0

x = 0

x = 0

x+3 = 0

x+3 = 0

x+3 = 0 // - 3

x = -3

x in (-oo:-3) U (-3:0) U (0:+oo)

4/x+1/x-1+3 = (9/(x+3))*(x-1) // - (9/(x+3))*(x-1)

4/x-((9/(x+3))*(x-1))+1/x-1+3 = 0

4/x-9*(x-1)*(x+3)^-1+1/x-1+3 = 0

(-9*(x-1))/(x+3)+4/x+1/x-1+3 = 0

(-9*x*(x-1))/(x*(x+3))+(4*(x+3))/(x*(x+3))+(1*(x+3))/(x*(x+3))+(-1*x*(x+3))/(x*(x+3))+(3*x*(x+3))/(x*(x+3)) = 0

4*(x+3)-9*x*(x-1)+1*(x+3)-1*x*(x+3)+3*x*(x+3) = 0

3*x^2-9*x^2-x^2+13*x+x-3*x+9*x+3+12 = 0

3*x^2-9*x^2-x^2+14*x-3*x+9*x+15 = 0

3*x^2-10*x^2+11*x+9*x+15 = 0

20*x-7*x^2+15 = 0

20*x-7*x^2+15 = 0

20*x-7*x^2+15 = 0

DELTA = 20^2-(-7*4*15)

DELTA = 820

DELTA > 0

x = (820^(1/2)-20)/(-7*2) or x = (-820^(1/2)-20)/(-7*2)

x = (2*205^(1/2)-20)/(-14) or x = (-2*205^(1/2)-20)/(-14)

(x-((2*205^(1/2)-20)/(-14)))*(x-((-2*205^(1/2)-20)/(-14))) = 0

((x-((2*205^(1/2)-20)/(-14)))*(x-((-2*205^(1/2)-20)/(-14))))/(x*(x+3)) = 0

((x-((2*205^(1/2)-20)/(-14)))*(x-((-2*205^(1/2)-20)/(-14))))/(x*(x+3)) = 0 // * x*(x+3)

(x-((2*205^(1/2)-20)/(-14)))*(x-((-2*205^(1/2)-20)/(-14))) = 0

( x-((-2*205^(1/2)-20)/(-14)) )

x-((-2*205^(1/2)-20)/(-14)) = 0 // + (-2*205^(1/2)-20)/(-14)

x = (-2*205^(1/2)-20)/(-14)

( x-((2*205^(1/2)-20)/(-14)) )

x-((2*205^(1/2)-20)/(-14)) = 0 // + (2*205^(1/2)-20)/(-14)

x = (2*205^(1/2)-20)/(-14)

x in { (-2*205^(1/2)-20)/(-14), (2*205^(1/2)-20)/(-14) }

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