Solve for X: Complex Rational Equation -8/(6(x+5)-2) = 1/(x+4)

Let's solve the equation step by step:

The given equation is:

$-\frac{8}{6 \times (x + 5) - 2} = \frac{1}{x + 4}$

To eliminate the fractions, we can use cross-multiplication:

$-8 \times (x + 4) = 1 \times (6 \times (x + 5) - 2)$

Expanding both sides yields:

$-8(x + 4) = 6(x + 5) - 2$

Distribute the terms:

$-8x - 32 = 6x + 30 - 2$

Simplifying the right-hand side:

$-8x - 32 = 6x + 28$

To solve for $x$, we isolate variables by moving terms with $x$ to one side:

Add $8x$ to both sides:

$-32 = 14x + 28$

Subtract 28 from both sides to further isolate the terms with $x$:

$-60 = 14x$

Finally, divide both sides by 14 to solve for $x$:

$x = -\frac{60}{14}$

This is the simplified form of $x$.

Therefore, the solution to the problem is:

$x = -\frac{60}{14}$.