$\text{Bài 4:}$
$a) \text{ĐKXĐ:}$
$• 2x+10 \ne 0 \to x\ne -5$
$• x \ne 0$
$• 2x(x+5) \ne 0 \to x\ne -5; 0$
$\text{Rút gọn:}$
$A=\dfrac{x^2+2x}{2x+10}+\dfrac{x-5}{x}+\dfrac{50-5x}{2x(x+5)}$
$\to A=\dfrac{x(x+2}{2(x+5)}+\dfrac{x-5}{x}+\dfrac{5(10-x)}{2x(x+5)}$
$\to A=\dfrac{x(x^2+2x+(x-5)(x+5)2+50-5x}{2x(x+5)}$
$\to A=\dfrac{x^3+2x^2+2x^2-50+50-5x}{2x(x+5)}$
$\to A==\dfrac{x^3+4x^2-5x}{2x(x+5)}$
$\to A=\dfrac{x(x^2+4x-5)}{2x(x+5)}$
$\to A=\dfrac{x(x^2-x+5x-5)}{2x(x+5)}$
$\to A=\dfrac{x[x(x-1)+5(x-1)]}{2x(x+5)}$
$\to A=\dfrac{x(x-1)(x+5)}{2x(x+5)}$
$\to A=\dfrac{x-1}{2}$
$b) \text{Để A=1}$
$\to \dfrac{x-1}{2}=1$
$x-1=2$
$\to x=3$
$\text{Để A=-3}$
$\to \dfrac{x-1}{2}=-3$
$\to x-1=-6$
$\to x=-5 (\text{không t/m điều kiện xác định})$.
