1. **State the problem:** Simplify the expression $$\frac{x^2+3x+2}{1-x^2}$$. 2. **Recall the formulas and rules:** - Factor quadratic expressions when possible. - Remember that $$1-x^2$$ is a difference of squares and can be factored as $$ (1-x)(1+x) $$. 3. **Factor the numerator:** $$x^2+3x+2 = (x+1)(x+2)$$ 4. **Factor the denominator:** $$1-x^2 = (1-x)(1+x)$$ 5. **Rewrite the expression with factors:** $$\frac{(x+1)(x+2)}{(1-x)(1+x)}$$ 6. **Notice that $$1-x$$ can be rewritten as $$-(x-1)$$, so:** $$1-x = -(x-1)$$ 7. **Rewrite denominator using this:** $$ (1-x)(1+x) = -(x-1)(1+x) $$ 8. **Now the expression is:** $$\frac{(x+1)(x+2)}{-(x-1)(x+1)}$$ 9. **Cancel the common factor $$(x+1)$$:** $$\frac{\cancel{(x+1)}(x+2)}{- (x-1)\cancel{(x+1)}} = \frac{x+2}{-(x-1)}$$ 10. **Simplify the negative sign in the denominator:** $$\frac{x+2}{-(x-1)} = -\frac{x+2}{x-1}$$ **Final answer:** $$-\frac{x+2}{x-1}$$