Question

Упростите выражение.
Пожалуйста помогите

Answer 1

$(\frac{1}{n(n-1)}+\frac{1}{n(n+1)}) : \frac{n+3}{n^2-1}  =\\(\frac{n+1+n-1}{n(n+1)(n-1)} ):\frac{n+3}{n^2-1}  =\\\\\frac{2n}{n(n^2-1)} : \frac{n+3}{n^2-1}=\\\frac{2n}{n(n^2-1)}*\frac{n^2-1}{n+3} = \frac{2n}{n}*\frac{1}{n+3}  =\frac{2}{n+3}$

Answer 2

Объяснение:

$\tt\displaystyle \[\left( {\frac{1}{{{n^2}-n}}+\frac{1}{{{n^2}+n}}}\right):\frac{{n+3}}{{{n^2}-1}}=\left( {\frac{{({n^2}+n)+({n^2}-n)}}{{({n^2}-n)({n^2}+n)}}} \right)*\frac{{{n^2}-1}}{{n+3}}=\frac{{2{n^2}}}{{{{\left( {{n^2}} \right)}^2}-{n^2}}}*\frac{{{n^2}-1}}{{n+3}}=\frac{{2{n^2}}}{{{n^4}-{n^2}}}*\frac{{{n^2}-1}}{{n+3}}=\frac{{2{n^2}}}{{{n^2}({n^2}-1)}}*\frac{{{n^2}-1}}{{n+3}}=\boxed{\frac{2}{{(n+3)}}}\]$