Ответ:

Объяснение:

1) = [tex]\frac{4n+m+n-m}{n^{2}-m^{2} }[/tex]=[tex]\frac{5n}{n^{2}-m^{2} }[/tex]

2) =[tex]\frac{a-6+3(a+2)}{a^{2} -4}[/tex]=[tex]\frac{a-6+3a+6}{a^{2} -4} =\frac{4a}{a^{2} -4}[/tex]

3) =[tex]\frac{x(x-5)-x^{2} }{(x-5)^{2}} =\frac{x^{2} -5x-x^{2} }{(x-5)^{2} } =-\frac{5x}{(x-5)^{2} }[/tex]

Ответ:

Применим формулы сокращённого умножения .

[tex]\displaystyle 1)\ \ \frac{4n+m}{n^2-m^2}+\frac{1}{n+m}=\frac{4n+m}{(n-m)(n+m)}+\frac{1}{n+m}=\frac{4n+m+(n-m)}{(n-m)(n+m)}=\\\\\\=\frac{5n}{(n-m)(n+m)}=\frac{5n}{n^2-m^2}\\\\\\2)\ \ \frac{a-6}{a^2-4}+\frac{3}{a-2}=\frac{a-6}{(a-2)(a+2)}+\frac{3}{a-2}=\frac{a-6+3(a+2)}{(a-2)(a+2)}=\\\\\\=\frac{4a}{(a-2)(a+2)}=\frac{4a}{a^2-4}[/tex]

[tex]\displaystyle 3)\ \ \frac{x}{x-5}-\frac{x^2}{x^2-10x+25}= \frac{x}{x-5}-\frac{x^2}{(x-5)^2}=\frac{x(x-5)-x^2}{(x-5)^2}=\\\\\\=\frac{x^2-5x-x^2}{(x-5)^2}=-\frac{5x}{(x-5)^2}[/tex]