Solve by multiplying each side by the other side's denominator:
\(\frac{8}{x - 4} = \frac{9}{6 + x}\)
\(8(6 + x) = 9(x - 4)\)
\(48 + 8x = 9x - 36\)
\(\bf x = 84\)
Now, something you should always check when you have x in the denominator of a fraction is to make sure that there isn't a problem with division by 0. Since neither of the fractions has a denominator of 0 when x = 84, there's no issue, so we're safe.
