Question

solve the equation 8/x-4=9/6+x

Answer 1

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.

Answer 2

$D:x\not =4 \wedge x\not=-6\\ \dfrac{8}{x-4}=\dfrac{9}{6+x}\\\\ 9(x-4)=8(6+x)\\ 9x-36=48+8x\\ x=84$