Giải bài 3 trang 48

Đề bài

Tính một cách hợp lí:

$a)\frac{x^2-49}{x^2+5}.\left(\frac{x^2+5}{x-7}-\frac{x^2+5}{x+7}\right)$

$b)\frac{19x+8}{x+1975}.\frac{2000-x}{x+1945}+\frac{19x+8}{x+1975}.\frac{2x-25}{x+1945}$

Lời giải chi tiết

$\begin{array}{c}a)\frac{x^2-49}{x^2+5}.\left(\frac{x^2+5}{x-7}-\frac{x^2+5}{x+7}\right)\\ =\frac{\left(x-7\right)\left(x+7\right)}{x^2+5}.\frac{x^2+5}{x-7}-\frac{\left(x-7\right)\left(x+7\right)}{x^2+5}.\frac{x^2+5}{x+7}\\ =x+7-\left(x-7\right)=14\end{array}$

$\begin{array}{c}b)\frac{19x+8}{x+1975}.\frac{2000-x}{x+1945}+\frac{19x+8}{x+1975}.\frac{2x-25}{x+1945}\\ =\frac{19x+8}{x+1975}.\left(\frac{2000-x}{x+1945}+\frac{2x-25}{x+1945}\right)\\ =\frac{19x+8}{x+1975}.\frac{2000-x+2x-25}{x+1945}\\ =\frac{19x+8}{x+1975}.\frac{x+1975}{x+1945}=\frac{19x+8}{x+1945}\end{array}$