A systems analyst at a logistics firm is standardizing two performance metrics represented by the expressions $\frac{2}{x^2-x-12}$ and $\frac{1}{x^2-16}$. After factoring the denominators, the analyst identifies that the first metric's denominator is $(x-4)(x+3)$. To rewrite this metric using the lowest common denominator (LCD) of $(x+3)(x-4)(x+4)$, which factor must be multiplied by both its numerator and denominator?

A financial analyst is standardizing two expense models for a quarterly report: Model A is $\frac{2}{x^2-x-12}$ and Model B is $\frac{1}{x^2-16}$. To compare them, they must be rewritten using the lowest common denominator (LCD) $(x+3)(x-4)(x+4)$. Arrange the steps for converting these models in the correct order.

A financial analyst is standardizing two budget models represented by the expressions $\frac{2}{x^2-x-12}$ and $\frac{1}{x^2-16}$. If the analyst rewrites both expressions to use the lowest common denominator $(x+3)(x-4)(x+4)$, then the rewritten numerator for the model $\frac{2}{x^2-x-12}$ is ${}2x+8$.

A logistics analyst is standardizing two data models used to calculate shipping efficiencies. Both models, represented by the rational expressions below, must be rewritten using the lowest common denominator (LCD) of $(x+3)(x-4)(x+4)$. Match each original expression with the specific polynomial factor it must be multiplied by to reach this common denominator.

A supply chain analyst is standardizing two freight cost models, represented by the expressions $\frac{2}{x^2-x-12}$ and $\frac{1}{x^2-16}$. To combine the models, they must be rewritten using the lowest common denominator $(x+3)(x-4)(x+4)$. When rewriting the first model, $\frac{2}{x^2-x-12}$, to use this common denominator, the fully simplified numerator is ____.