$a)\frac{{47}^2-{23}^2}{{59}^2-{11}^2}=\frac{\left(47-23\right)\cdot \left(47+23\right)}{\left(59-11\right)\cdot \left(59+11\right)}=\frac{24\cdot 70}{48\cdot 70}=\frac{24}{48}=\frac{1}{2}$

$b)\frac{{68}^2-{34}^2}{{67}^2-{33}^2}=\frac{\left(68-34\right)\cdot \left(68+34\right)}{\left(67-33\right)\cdot \left(67+33\right)}=\frac{34\cdot 102}{34\cdot 100}=\frac{102}{100}=\frac{51}{50}=1\frac{1}{50}$

$c)\frac{{78}^2-{22}^2}{{114}^2-{86}^2}=\frac{\left(78-22\right)\cdot \left(78+22\right)}{\left(114-86\right)\cdot \left(114+86\right)}=\frac{{\sout{56}}^2\cdot 100}{{\sout{28}}^1\cdot 200}=\frac{2\cdot 100}{200}=\frac{200}{200}=1$