Find the value of (7C3 + 7C6) / (7C3 - 7C6)

The formula for combinations is $_nC_r = \frac{n!}{r!(n-r)!}$.

$${_7C_3} = \frac{7!}{3!(7-3)!} = \frac{7!}{3!4!}$$ $${_7C_3} = \frac{7 \times 6 \times 5 \times 4!}{3 \times 2 \times 1 \times 4!} = \frac{7 \times 6 \times 5}{3 \times 2 \times 1} = \frac{210}{6} = 35$$

Using the combination formula:

$${_7C_6} = \frac{7!}{6!(7-6)!} = \frac{7!}{6!1!}$$ $${_7C_6} = \frac{7 \times 6!}{6! \times 1} = 7$$

Alternatively, we can use the property $_nC_r = {_nC_{n-r}}$, so $_7C_6 = {_7C_{7-6}} = {_7C_1} = 7$.

The expression is $\frac{{_7C_3} + {_7C_6}}{{_7C_3} - {_7C_6}}$.

$$\frac{35 + 7}{35 - 7}$$

Both the numerator and the denominator are divisible by 14.

$$\frac{42 \div 14}{28 \div 14} = \frac{3}{2}$$

The value of the expression is:

\boxed{\textbf{\frac{3}{2}}}