To solve these equations, we can first simplify them by multiplying both sides by the denominator to get rid of the fractions:

For the first equation:

3/14 = 21/2(x + 31)

3/14 * 2/21 = x + 31

1/14 = x + 31

x = 1/14 - 31

x = -2187/14

For the second equation:

9/10 = 63/5(x + 8)

9/10 * 5/63 = x + 8

1/14 = x + 8

x = 1/14 - 8

x = -111/14

Therefore, the solutions to the equations are x = -2187/14 and x = -111/14.