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The common denominator of the two fractions is: 572

$ \frac{31}{52 }= \frac{(11*31)}{(11*52)} =\frac{ 341}{572} $

$ \frac{17}{44 }= \frac{(13*17)}{(13*44)} =\frac{ 221}{572} $

Fractions adjusted to a common denominator

$ \frac{31}{52 }-\frac{ 17}{44 }=\frac{ 341}{572 }-\frac{ 221}{572} $

$ \frac{341}{572 }-\frac{ 221}{572 }= \frac{(341-221)}{572} $

$ \frac{(341-221)}{572 }=\frac{ 120}{572} $

$ \frac{120}{572 }=\frac{ 30}{143} $

$ $

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