Roots of sum of reciprocals

Algebra Level 3

1x1+1x2+1x3+1x4+1x5=1 \frac1{x-1}+\frac1{x-2}+\frac1{x-3}+\frac1{x-4}+\frac1{x-5} = 1

What is the number of real roots to the equation above in the interval [1,5][1,5]?

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