Question

Розвяжіть приклад на фото за один приклад даю 100 балів

Answer 1

$\displaystyle\bf\\\Big(n+\frac{1}{2+n} \Big):\frac{n+1}{n+2} -n=\frac{2n+n^{2} +1}{2+n} \cdot\frac{n+2}{n+1} -n=\\\\\\=\frac{(n+1)^{2} }{2+n} \cdot\frac{n+2}{n+1} -n=n+1-n=1$

Answer 2

$\displaystyle\bigg(n+\dfrac{1}{2+n}\bigg):\dfrac{n+1}{n+2}-n=\dfrac{n(2+n)+1}{2+n}\cdot\dfrac{n+2}{n+1}-n=\\\\\\\displaystyle=\dfrac{2n+n^2+1}{n+2}\cdot\dfrac{n+2}{n+1}-n=\dfrac{n^2+2n+1}{n+1}-n=\dfrac{(n+1)^2}{n+1}-n=\\\\\\\displaystyle=n+1-n=1$