<s>[INST] Reducing fractions How can I get  [if it's possible]:
$$ 2- \frac{1}{n+1} $$
from this: 
$$2- \frac{1}{n} + \frac{1}{n(n+1)} $$
EDIT:
I started like this:
$$2- \frac{1}{n} + \frac{1}{n(n+1)}= 2-\frac{n+1}{n(n+1)}+\frac{1}{n(n+1)} =2-\frac{n+2}{n(n+1)}  $$
How do I proceed from here?
 [/INST] 
I started like this: $$2- \frac{1}{n} + \frac{1}{n(n+1)}=
 2-\frac{n+1}{n(n+1)}+\frac{1}{n(n+1)} =2-\frac{n+2}{n(n+1)}  $$

The mistake happened here:
$$2-\frac{n+1}{n(n+1)}+\frac{1}{n(n+1)} =2-\frac{n+2}{n(n+1)}$$
because you forgot the minus sign. You can rewrite the left hand side as
$$2 +\frac{-n-1}{n(n+1)} + \frac{1}{n(n+1)}$$ and continue from there.
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