109. Упростите выражение: 1) (4x−y)/(x²−y²) + 1/(x−y); 2) y²/(y²−81) − y/(y+9); 3) 10a/(25a²−9) − 1/(5a+3); 4) n/(n−7) − n²/(n²−14n+49).

\(x^2-y^2=(x-y)(x+y)\).

\(\frac{4x-y}{x^2-y^2}+\frac{1}{x-y}=\frac{4x-y+x+y}{(x-y)(x+y)}=\frac{5x}{x^2-y^2}\), где \(x\ne\pm y\).

\(y^2-81=(y-9)(y+9)\).

\(\frac{y^2}{y^2-81}-\frac{y}{y+9}=\frac{y^2-y(y-9)}{(y-9)(y+9)}=\frac{9y}{y^2-81}\), где \(y\ne\pm9\).

\(25a^2-9=(5a-3)(5a+3)\).

\(\frac{10a}{25a^2-9}-\frac{1}{5a+3}=\frac{10a-(5a-3)}{(5a-3)(5a+3)}=\frac{1}{5a-3}\), где \(a\ne\pm\frac35\).

\(n^2-14n+49=(n-7)^2\).

\(\frac{n}{n-7}-\frac{n^2}{n^2-14n+49}=\frac{n(n-7)-n^2}{(n-7)^2}=-\frac{7n}{(n-7)^2}\), где \(n\ne7\).