simp (2)/(x+4)-(x-12)/(x^2)-16

To simplify the given expression, we need to find a common denominator for the two fractions. The common denominator is the product of the two denominators, which is $(x+4)(x^2-16)$.<br /><br />Now, let's rewrite the expression with the common denominator:<br /><br />$\frac{2}{x+4} \cdot \frac{x^2-16}{x^2-16} - \frac{x-12}{x^2-16} \cdot \frac{x+4}{x+4}$<br /><br />Simplifying the numerators, we get:<br /><br />$\frac{2(x^2-16)}{(x+4)(x^2-16)} - \frac{(x-12)(x+4)}{(x+4)(x^2-16)}$<br /><br />Combining the fractions, we have:<br /><br />$\frac{2(x^2-16) - (x-12)(x+4)}{(x+4)(x^2-16)}$<br /><br />Expanding the numerators, we get:<br /><br />$\frac{2x^2 - 32 - (x^2 - 16x - 12x - 48)}{(x+4)(x^2-16)}$<br /><br />Simplifying further, we have:<br /><br />$\frac{2x^2 - 32 - x^2 + 16x + 12x + 48}{(x+4)(x^2-16)}$<br /><br />Combining like terms, we get:<br /><br />$\frac{x^2 + 28x + 16}{(x+4)(x^2-16)}$<br /><br />Therefore, the simplified expression is $\frac{x^2 + 28x + 16}{(x+4)(x^2-16)}$.