Question

Упростите выражение n+6/4n+8 - n+2/4n-8+3/n^2-4

Answer 1

$\dfrac{n+6}{4n+8}-\dfrac{n+2}{4n-8}+\dfrac{3}{n^2-4}=\dfrac{n+6}{4(n+2)}-\dfrac{n+2}{4(n-2)}+\dfrac{3}{(n-2)(n+2)}=\\ \\ \\ =\dfrac{(n+6)(n-2)-(n+2)^2+3\cdot 4}{4(n+2)(n-2)}=\dfrac{n^2+4n-12-n^2-4n-4+12}{4(n+2)(n-2)}=\\ \\ \\ =-\dfrac{4}{4(n+2)(n-2)}=-\dfrac{1}{4(n^2-4)}=-\dfrac{1}{n^2-4}$