Subtract. \[ -\frac{8 a+5 x}{2 a}-\frac{4 a-6 x}{2 a} \] Simplify your answer as much as possible.
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To simplify the expression \[ -\frac{8 a + 5 x}{2 a} - \frac{4 a - 6 x}{2 a}, \] we can combine the fractions since they have the same denominator. First, we write the expression as: \[ -\left(\frac{8 a + 5 x}{2 a} + \frac{4 a - 6 x}{2 a}\right). \] Now, combine the terms in the numerator: \[ -\frac{(8 a + 5 x) + (4 a - 6 x)}{2 a} = -\frac{8 a + 5 x + 4 a - 6 x}{2 a}. \] Combining like terms in the numerator gives us: \[ 8 a + 4 a = 12 a, \quad \text{and} \quad 5 x - 6 x = -1 x. \] So, we have: \[ -\frac{12 a - x}{2 a}. \] Now, we can distribute the negative sign: \[ \frac{-(12 a - x)}{2 a} = \frac{-12 a + x}{2 a} = \frac{x - 12 a}{2 a}. \] Thus, the simplified form of the expression is: \[ \frac{x - 12 a}{2 a}. \]
