_12/19×38/45; -15/22×(-5/11)

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Let's solve each of these separately.

( \frac{12}{19} \times \frac{38}{45}
To multiply fractions, multiply the numerators together and the denominators together
( \frac{12}{19} \times \frac{38}{45} = \frac{12 \times 38}{19 \times 45}
( = \frac{456}{855}
Simplifying the fraction, we get
( = \frac{304}{573} )

( -\frac{15}{22} \times -\frac{5}{11}
When multiplying two negative fractions, the result will be positive
( -\frac{15}{22} \times -\frac{5}{11} = \frac{15}{22} \times \frac{5}{11}
( = \frac{15 \times 5}{22 \times 11}
( = \frac{75}{242} )

Therefore, the final result is ( \frac{304}{573} + \frac{75}{242} ).