Question

tính nhanh biểu thức

Answer 1

Biểu thức nào nhỉ cậu?

Answer 2

Lời giải:
$Q(x)=\frac{1}{(x-1)(x+1)}+\frac{1}{(x+1)(x+3)}+\frac{1}{(x+3)(x+5)}+\frac{1}{(x+5)(x+7)}$

$2Q(x)=\frac{2}{(x-1)(x+1)}+\frac{2}{(x+1)(x+3)}+\frac{2}{(x+3)(x+5)}+\frac{2}{(x+5)(x+7)}$

$=\frac{1}{x-1}-\frac{1}{x+1}+\frac{1}{x+1}-\frac{1}{x+3}+\frac{1}{x+3}-\frac{1}{x+5}+\frac{1}{x+5}-\frac{1}{x+7}$

$=\frac{1}{x-1}-\frac{1}{x+7}=\frac{8}{(x-1)(x+7)}$

$\Rightarrow Q(x)=\frac{4}{(x-1)(x+7)}$