Given the equation:
$$\frac{- \frac{1}{y} + \frac{8}{x}}{\frac{1}{y} + \frac{8}{x}} = 0$$
transform:
Take common factor from the equation
$$- \frac{x - 8 y}{x + 8 y} = 0$$
the denominator
$$x + 8 y$$
then
x is not equal to -8*y
Because the right side of the equation is zero, then the solution of the equation is exists if at least one of the multipliers in the left side of the equation equal to zero.
We get the equations
$$- x + 8 y = 0$$
solve the resulting equation:
1.
$$- x + 8 y = 0$$
Looking for similar summands in the left part:
-x + 8*y = 0
Move the summands with the other variables
from left part to right part, we given:
$$- x = - 8 y$$
Divide both parts of the equation by -1
x = -8*y / (-1)
We get the answer: x1 = 8*y
but
x is not equal to -8*y
The final answer:
$$x_{1} = 8 y$$