\(a,\frac{6\cdot9-2\cdot18}{53\cdot3-126}=\frac{2\cdot3\cdot3\cdot3-2\cdot3\cdot3\cdot2}{53\cdot3-53\cdot2}\)
\(=\frac{2\cdot3^3-2^2\cdot3^2}{53\cdot3-53\cdot2}=\frac{2\cdot3^2\cdot\left(3-2\right)}{53\cdot\left(3-2\right)}\)
\(=\frac{2\cdot9}{53}=\frac{18}{53}\)
\(b,\frac{21\cdot17-5\cdot17}{19\cdot20-40}=\frac{21\cdot17-5\cdot17}{19\cdot20-2\cdot20}\)
\(=\frac{17\left(21-5\right)}{20\cdot\left(19-2\right)}=\frac{17\cdot16}{20\cdot17}\)
\(=\frac{16}{20}=\frac{4}{5}\)
a, \(\frac{6.9-2.18}{53.3-126}=\frac{2.3.3.3-2.3.3.2}{53.3-53.2}\)
\(=\frac{2.3^3-2^2.3^2}{53.3-53.2}=\frac{2.3^2.\left(3-2\right)}{53.\left(3-2\right)}\)
\(=\frac{2.9}{53}=\frac{18}{53}\)
b, \(\frac{21.17-6.17}{19.20-40}=\frac{21.17-6.17}{19.20-2.20}\)
\(=\frac{17\left(21-6\right)}{20\left(19-2\right)}=\frac{17.15}{20.17}\)
\(=\frac{15}{20}=\frac{3}{4}\)
Study well ! >_<
