Convert the mixed numbers to improper fractions: 17/8*27/8-35/16*59/16=459/64-2065/256.
1836/256-2065/256=-229/256. The difference is 229/256 (the sign depends on which way you do the subtraction).
[To convert a mixed number to an improper fraction, let's write a mixed number as A b/c and convert it: (cA+b)/c. In words, multiply the whole part of the mixed number by the fraction denominator and add on its numerator; then write the result over the denominator. To convert 459/64 to 1836/256 I just multiplied top and bottom by 4. The reason for this conversion was to put both fractions over the same denominator to do the arithmetic: 1836/256-2065/256 is (1836-2065)/256=-229/256.]