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The common denominator of the two fractions is: 10

$ \frac{(x+2)}{2 }= \frac{(5*(x+2))}{(2*5)} = \frac{(5*(x+2))}{10} $

$ \frac{(x+1)}{5 }= \frac{(2*(x+1))}{(2*5)} = \frac{(2*(x+1))}{10} $

Fractions adjusted to a common denominator

$ \frac{(x+2)}{2 }+ \frac{(x+1)}{5 }= \frac{(5*(x+2))}{10 }+ \frac{(2*(x+1))}{10} $

$ \frac{(5*(x+2))}{10 }+ \frac{(2*(x+1))}{10 }= \frac{(5*(x+2)+2*(x+1))}{10} $

$ \frac{(5*(x+2)+2*(x+1))}{10 }= \frac{(5*(x+2)+2*(x+1))}{10} $

$ $

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