Simplify the following by factoring and canceling. $$ \frac{x^{2}-9}{3-x} $$

Question

UpStudy AI · Accepted Answer

1. Factor the numerator as a difference of two squares:
   $$
   x^2 - 9 = (x-3)(x+3)
   $$

2. Rewrite the expression with the factored numerator:
   $$
   \frac{(x-3)(x+3)}{3-x}
   $$

3. Notice that the denominator $$3-x$$ can be rewritten as:
   $$
   3 - x = -(x-3)
   $$

4. Substitute this into the expression:
   $$
   \frac{(x-3)(x+3)}{-(x-3)}
   $$

5. Cancel the common factor $$x-3$$ (provided $$x \neq 3$$):
   $$
   = - (x+3)
   $$

The simplified expression is:
$$
-(x+3) \quad (\text{with } x \neq 3)
$$
The simplified expression is $$-(x + 3)$$ (where $$x \neq 3$$).

Simplify the following by factoring and canceling.