Question

Подайте вираз у вигляді дробу​

Answer 1

Решение:

$1)~~~\dfrac{4n+m}{n^2 - m^2} +\dfrac{1}{n+m} = \dfrac{4n+m}{(n-m)(n+m)} +\dfrac{1}{n+m} = \\ \\=\dfrac{4n+m+n-m}{(n-m)(n+m)} =\dfrac{5n}{n^2-m^2} .$

$2)~~~~~\dfrac{a-6}{a^2-4} + \dfrac{3}{a-2} = \dfrac{a-6}{(a-2)(a+2)} + \dfrac{3}{a-2} = \\ \\=\dfrac{a-6+3(a+2)}{(a-2)(a+2)} =\dfrac{a-6+3a+6}{(a-2)(a+2)} =\dfrac{4a}{a^2-4} .$

$3)~~~~~\dfrac{x}{x-5} - \dfrac{x^2}{x^2-10x+25} =\dfrac{x}{x-5} - \dfrac{x^2}{(x-5)^2} =\\ \\=\dfrac{x(x-5) -x^2}{(x-5)^2} =\dfrac{x^2-5x -x^2}{(x-5)^2} =-\dfrac{5x}{(x-5)^2} .$