Bài 43. Thực hiện các phép tính sau:
a) \( \frac{5x-10}{x^{2}+7}\) : (2x - 4) b) (x2 -25) : \( \frac{2x+10}{3x-7}\)
c) \( \frac{x^{2}+x}{5x^{2}-10x+5}:\frac{3x+3}{5x-5}\).
Hướng dẫn giải:
a) \( \frac{5x-10}{x^{2}+7}\) : (2x - 4) \( =\frac{5x-10}{x^{2}+7}:\frac{2x-4}{1}=\frac{5x-10}{x^{2}+7}.\frac{1}{2x-4}\)
\( =\frac{5(x-2).1}{(x^{2}+7).2(x-2)}=\frac{5}{2(x^{2}+7)}\)
b) (x2 -25) : \( \frac{2x+10}{3x-7}\) \( =\frac{x^{2}-25}{1}:\frac{2x+10}{3x-7}=\frac{x^{2}-25}{1}.\frac{3x-7}{2x+10}\)
\( =\frac{(x-5)(x+5)(3x-7)}{2(x+5)}=\frac{(x-5)(3x+7)}{2}\)
c) \( \frac{x^{2}+x}{5x^{2}-10x+5}:\frac{3x+3}{5x-5}\) \( \frac{x^{2}+x}{5x^{2}-10x+5}.\frac{5x-5}{3x+3}=\frac{x(x+1).5(x-1)}{5(x-1)^{2}}=\frac{x}{3(x-1)}\)