1. **State the problem:** Simplify the expression $$\frac{y^2 - 36}{5y^2 - 26y - 24}$$. 2. **Recall the formula and rules:** To simplify a rational expression, factor both numerator and denominator and then cancel any common factors. 3. **Factor the numerator:** $$y^2 - 36 = (y - 6)(y + 6)$$ (difference of squares). 4. **Factor the denominator:** We need to factor $$5y^2 - 26y - 24$$. Find two numbers that multiply to $$5 \times (-24) = -120$$ and add to $$-26$$. These numbers are $$-30$$ and $$4$$. Rewrite the middle term: $$5y^2 - 30y + 4y - 24$$ Group terms: $$(5y^2 - 30y) + (4y - 24)$$ Factor each group: $$5y(y - 6) + 4(y - 6)$$ Factor out common binomial: $$(5y + 4)(y - 6)$$ 5. **Rewrite the expression with factors:** $$\frac{(y - 6)(y + 6)}{(5y + 4)(y - 6)}$$ 6. **Cancel common factors:** $$\frac{\cancel{(y - 6)}(y + 6)}{(5y + 4)\cancel{(y - 6)}}$$ 7. **Final simplified expression:** $$\frac{y + 6}{5y + 4}$$ This is the simplified form of the original expression, valid for $$y \neq 6$$ (to avoid division by zero).