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Algebra Level pending

Find the number real \(x\) satisfying the equation below.

\[\dfrac{x^{16}-16 x^{15}+120 x^{14}-560 x^{13}+1820 x^{12}-4368 x^{11}+8008 x^{10}-11440 x^9+12870 x^8-11440 x^7+8008 x^6-4368 x^5+1820 x^4-560 x^3+120 x^2-16 x+1}{x^{15}-15 x^{14}+105 x^{13}-455 x^{12}+1365 x^{11}-3003 x^{10}+5005 x^9-6435 x^8+6435 x^7-5005 x^6+3003 x^5-1365 x^4+455 x^3-105 x^2+15 x-1}=0\]

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