Divide the sum of -2 15/17 and 3 5/34 by their difference.

Given rational numbers are -49/17 and 107/34

Sum of the given numbers:

= (-49/17) + (107/34)

= (-49 × 2)/(17 × 2) + (107 × 1)/(34 × 1) [LCM of 17 and 34 = 34]

= (-98/34) + (107/34) = (-98 + 107)/34 = 9/34

Difference of the given numbers:

= 107/34 − (−49/17)

= (107/34) + (49/17) = (107 × 1)/(34 × 1) + (49 × 2)/(17 × 2)

= (107/34) + (98/34) = (107 + 98)/34 = 205/34

As per the question:

Sum of the numbers ÷ Difference of the numbers

= (9/34) ÷ (205/34) = (9/34) × (34/205) = 9/205

Hence, the required division = 9/205.