4/(4-x)=-x

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Solution for 4/(4-x)=-x equation: 


D( x )

4-x = 0

4-x = 0

4-x = 0

4-x = 0 // - 4

-x = -4 // * -1

x = 4

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

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

4/(4-x)+x = 0

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

x*(4-x)+4 = 0

4*x-x^2+4 = 0

4*x-x^2+4 = 0

4*x-x^2+4 = 0

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

DELTA = 32

DELTA > 0

x = (32^(1/2)-4)/(-1*2) or x = (-32^(1/2)-4)/(-1*2)

x = (4*2^(1/2)-4)/(-2) or x = (-4*2^(1/2)-4)/(-2)

(x-((4*2^(1/2)-4)/(-2)))*(x-((-4*2^(1/2)-4)/(-2))) = 0

((x-((4*2^(1/2)-4)/(-2)))*(x-((-4*2^(1/2)-4)/(-2))))/(4-x) = 0

((x-((4*2^(1/2)-4)/(-2)))*(x-((-4*2^(1/2)-4)/(-2))))/(4-x) = 0 // * 4-x

(x-((4*2^(1/2)-4)/(-2)))*(x-((-4*2^(1/2)-4)/(-2))) = 0

( x-((-4*2^(1/2)-4)/(-2)) )

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

x = (-4*2^(1/2)-4)/(-2)

( x-((4*2^(1/2)-4)/(-2)) )

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

x = (4*2^(1/2)-4)/(-2)

x in { (-4*2^(1/2)-4)/(-2), (4*2^(1/2)-4)/(-2) }

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