X/x-8-6/x-2=36/(x-2)(x-8)

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Solution for X/x-8-6/x-2=36/(x-2)(x-8) equation:


D( x )

x-2 = 0

x = 0

x-2 = 0

x-2 = 0

x-2 = 0 // + 2

x = 2

x = 0

x = 0

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

X/x-(6/x)-8-2 = (36/(x-2))*(x-8) // - (36/(x-2))*(x-8)

X/x-((36/(x-2))*(x-8))-(6/x)-8-2 = 0

X/x-36*(x-2)^-1*(x-8)-6*x^-1-8-2 = 0

(-36*(x-8))/(x-2)+X/x-6/x-8-2 = 0

(-36*x*(x-8))/(x*(x-2))+(X*(x-2))/(x*(x-2))+(-6*(x-2))/(x*(x-2))+(-8*x*(x-2))/(x*(x-2))+(-2*x*(x-2))/(x*(x-2)) = 0

X*(x-2)-36*x*(x-8)-6*(x-2)-8*x*(x-2)-2*x*(x-2) = 0

X*x-2*X-36*x^2-8*x^2-2*x^2+288*x-6*x+16*x+4*x+12 = 0

X*x-2*X-36*x^2-8*x^2-2*x^2+282*x+16*x+4*x+12 = 0

X*x-2*X-44*x^2-2*x^2+298*x+4*x+12 = 0

X*x-2*X-46*x^2+302*x+12 = 0

(X*x-2*X-46*x^2+302*x+12)/(x*(x-2)) = 0

(X*x-2*X-46*x^2+302*x+12)/(x*(x-2)) = 0 // * x*(x-2)

X*x-2*X-46*x^2+302*x+12 = 0

302*x-2*X-46*x^2+12 = 0

DELTA = 302^2-(-46*4*(12-2*X))

DELTA = 184*(12-2*X)+91204

184*(12-2*X)+91204 = 0

184*(12-2*X)+91204 = 0

93412-368*X = 0

93412-368*X = 0

93412-368*X = 0 // - 93412

-368*X = -93412 // : -368

X = -93412/(-368)

X = 23353/92

DELTA = 0 <=> t_3 = 23353/92

x = -302/(-46*2) i X = 23353/92

x = 151/46 i X = 23353/92

( x = ((184*(12-2*X)+91204)^(1/2)-302)/(-46*2) or x = (-(184*(12-2*X)+91204)^(1/2)-302)/(-46*2) ) i X > 23353/92

( x = ((184*(12-2*X)+91204)^(1/2)-302)/(-92) or x = ((184*(12-2*X)+91204)^(1/2)+302)/92 ) i X > 23353/92

X-23353/92 > 0

X-23353/92 > 0 // + 23353/92

X > 23353/92

x in { 151/46, ((184*(12-2*X)+91204)^(1/2)-302)/(-92), ((184*(12-2*X)+91204)^(1/2)+302)/92 }

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