Rút gọn rồi quy đồng mẫu các phân số sau :
a) \(\dfrac{{ - 15}}{{90}},\dfrac{{100}}{{500}}\) và \(\dfrac{{75}}{{ - 225}}\) ;
b) \(\dfrac{{120}}{{40}},\dfrac{{ - 280}}{{600}}\) và \(\dfrac{{ - 18}}{{75}}\)
\(\eqalign{ & {{ - 15} \over {90}} = {{ - 15:15} \over {90:15}} = {{ - 1} \over 6}, \cr & {{100} \over {500}} = {{100:100} \over {500:100}} = {1 \over 5}, \cr & {{75} \over { - 225}} = {{ - 75} \over {225}} = {{ - 75:75} \over {225:75}} = {{ - 1} \over 3}. \cr & BCNN(6;5;3) = 30 \cr} \)
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Do đó:
\(\eqalign{
& \frac{{ - 15}}{{90}} = \frac{{ - 1}}{6} = \frac{{ - 1.5}}{{6.5}} = \frac{{ - 5}}{{30}}; \cr
& \frac{{100}}{{500}} = \frac{1}{5} = \frac{{1.6}}{{5.6}} = \frac{6}{{30}}; \cr
& \frac{{75}}{{ - 225}} = \frac{{ - 1}}{3} = \frac{{ - 1.10}}{{3.10}} = \frac{{ - 10}}{{30}}. \cr} \)
\(\eqalign{ & b){{120} \over {40}} = {{120:40} \over {40:40}} = {3 \over 1}, \cr & {{ - 280} \over {600}} = {{ - 280:40} \over {600:40}} = {{ - 7} \over {15}}, \cr & {{ - 18} \over { - 75}} = {{18} \over {75}} = {{18:3} \over {75:3}} = {6 \over {25}}. \cr} \)
Do đó:
\(\eqalign{
& \frac{{120}}{{40}} = \frac{3}{1} = \frac{{3.75}}{{1.75}} = \frac{{225}}{{75}}; \cr
& \frac{{ - 280}}{{600}} = \frac{{ - 7}}{{15}} = \frac{{ - 7.5}}{{15.5}} = \frac{{ - 35}}{{75}}; \cr
& \frac{{ - 18}}{{ - 75}} = \frac{{18}}{{75}} = \frac{6}{{25}} = \frac{{6.3}}{{25.3}} = \frac{{18}}{{75}}. \cr} \)