(29 * 70 - 60 * 29 + 90 * 29)/(87 * 78 + 177 * 87 + 745 * 87)

To simplify the expression \((29 * 70 - 60 * 29 + 90 * 29)/(87 * 78 + 177 * 87 + 745 * 87)\), we can start by factoring out common terms. First, for the numerator: \[ 29 * 70 - 60 * 29 + 90 * 29 \] We can factor out \(29\): \[ 29 * (70 - 60 + 90) = 29 * (70 + 30) = 29 * 100 = 2900 \] Now let's look at the denominator: \[ 87 * 78 + 177 * 87 + 745 * 87 \] Again, we can factor out \(87\): \[ 87 * (78 + 177 + 745) = 87 * (78 + 177 + 745) = 87 * 1000 = 87000 \] Now, we can put the simplified numerator and denominator together: \[ \frac{2900}{87000} \] We can simplify this fraction by reducing it: \[ \frac{2900 \div 2900}{87000 \div 2900} = \frac{1}{30} \] Thus, the final result is: \[ \boxed{\frac{1}{30}} \]