(d) 1\(\frac1{24}\)
\(\frac{1\frac17-\frac23+\frac{\frac25}{1-\frac{1}{25}}}{1 -\frac17\bigg(\frac13+\frac{\frac25}{1-\frac25}\bigg)}\) = \(\frac{\frac87-\frac23+\frac{\frac25}{\frac{24}{25}}}{1 -\frac17\bigg(\frac13+\frac{\frac25}{\frac35}\bigg)}\)
= \(\frac{\frac87-\frac23+\frac25\times\frac{25}{24}}{1-\frac17\big(\frac13+\frac23\big)}\)
= \(\frac{\frac87-\frac23+\frac{5}{12}}{1-\frac17}\) = \(\frac{\frac{96-56+35}{84}}{\frac67}\)
= \(\frac{75}{84}\times\frac76=\frac{25}{24}=\) 1\(\frac1{24}\)