Упростить выражение:a) [latex] \frac{2}{x-y} + \frac{x-y}{xy} [/latex]b) [latex] \frac{p-1}{p+2} - \frac{p+1}{p-2} [/latex]c) [latex] \frac{8m-n}{mn- m^{2} } - \frac{m-8n}{mn- n^{2} } [/latex]

[latex] \frac{2}{x-y} + \frac{x-y}{xy} [/latex] = [latex] \frac{2xy + (x-y)^2}{xy(x-y)}[/latex] = [latex] \frac{x^2 + y^2}{x^2y - xy^2}[/latex] = [latex] \frac{x^2 + y^2}{xy(x - y)} [/latex] = [latex] \frac{2xy + (x - y)^2}{xy(x - y)}[/latex] = [latex] \frac{x^2 + y^2}{xy(x - y)}[/latex] [latex] \frac{p-1}{p+2} - \frac{p+1}{p-2} [/latex] = [latex] \frac{(-p - 1)(p + 2) + (p - 2)(p - 1)}{(p - 2)(p + 2)}[/latex] = [latex] \frac{-6p}{(p - 2)(p + 2)}[/latex] = [latex] \frac{-6p}{p^2 - 4}[/latex] [latex] \frac{8m-n}{mn- m^{2} } - \frac{m-8n}{mn- n^{2} } [/latex] = [latex] \frac{(-m + 8n)(-m^2 + mn) + (8m - n)(mn - n^2)}{(-m^2 + mn)(mn - n^2)}[/latex] = [latex] \frac{-(m + n)}{mn}[/latex]