Evaluate the following:

(-12)/(-5)+7/(-3)+(-5)/14+22/7

We start with the expression:

(-12/5) + (7 / -3) + (-5/14) + (22/7)

= (12/5) − (7/3) − (5/14) + (22/7)

[LCM of 5, 3, 14, and 7 = 210]

Now converting each fraction to have denominator 210:

(12/5) = (12 × 42)/(5 × 42) = 504/210

(−7/3) = (−7 × 70)/(3 × 70) = −490/210

(−5/14) = (−5 × 15)/(14 × 15) = −75/210

(22/7) = (22 × 30)/(7 × 30) = 660/210

So, (12/5) − (7/3) − (5/14) + (22/7) = (504 − 490 − 75 + 660)/210

= (1164 − 565)/210 = 599/210

Hence, the required rational number = 599/210