QuestionSimplify $\frac{x-3}{x-4}-\frac{6 x-16}{x^{2}-16}$

Studdy Solution
The simplified expression is:
$$\frac{x^2 - 5x + 4}{(x-4)(x+4)}$$
Check if the numerator can be factored further:
The numerator $x^2 - 5x + 4$ factors to:
$$(x - 4)(x - 1)$$
Thus, the expression becomes:
$$\frac{(x - 4)(x - 1)}{(x-4)(x+4)}$$
Cancel the common factor $(x - 4)$:
$$\frac{x - 1}{x + 4}$$
The simplified expression is:
$$\frac{x - 1}{x + 4}$$