Câu 4: Trang 46 toán VNEN 8 tập 1
Thực hiện các phép tính sau:
a) $\frac{(x + y)^{2}}{x^{2} + xy}$ + $\frac{(x – y)^{2}}{x^{2} – xy}$ + 7; b) $\frac{x^{2} – 4x}{xy – 4x – 3y + 12}$ + $\frac{x – 2}{y – 4}$; c) $\frac{y^{2}}{xy – 5x + y - 5}$ + $\frac{2}{x + 1}$.
Bài Làm:
a) $\frac{(x + y)^{2}}{x^{2} + xy}$ + $\frac{(x – y)^{2}}{x^{2} – xy}$ + 7 = $\frac{(x + y)^{2}}{x(x + y)}$ + $\frac{(x – y)^{2}}{x(x – y)}$ + 7 = $\frac{x + y}{x}$ + $\frac{x - y}{x}$ + $\frac{7x}{x}$ = $\frac{x + y + x – y + 7x}{x}$ = $\frac{9x}{x}$ = 9;
b) $\frac{x^{2} – 4x}{xy – 4x – 3y + 12}$ + $\frac{x – 2}{y – 4}$ = $\frac{2y}{x(2x – y)}$ + $\frac{-4x}{x(2x – y)}$ = $\frac{2y – 4x}{x(2x – y)}$;
c) $\frac{y^{2}}{xy – 5x + y - 5}$ + $\frac{2}{x + 1}$ = $\frac{y^{2}}{(y – 5)(x + 1)}$ + $\frac{2}{x + 1}$ = $\frac{y^{2}}{(y – 5)(x + 1)}$ + $\frac{2(y – 5)}{(x + 1)(y – 5)}$ = $\frac{y^{2} + 2y – 10}{(y – 5)(x + 1)}$.