1. **State the problem:** Solve the equation $$\frac{x^2 + x - 30}{x - 5} = 1$$ for $x$. 2. **Recall the formula and rules:** To solve rational equations, multiply both sides by the denominator to eliminate the fraction, but remember $x \neq 5$ because the denominator cannot be zero. 3. **Multiply both sides by $x - 5$:** $$\frac{x^2 + x - 30}{x - 5} \times (x - 5) = 1 \times (x - 5)$$ which simplifies to $$x^2 + x - 30 = x - 5$$ 4. **Bring all terms to one side:** $$x^2 + x - 30 - x + 5 = 0$$ which simplifies to $$x^2 - 25 = 0$$ 5. **Recognize the difference of squares:** $$x^2 - 25 = (x - 5)(x + 5) = 0$$ 6. **Solve for $x$:** Set each factor equal to zero: $$x - 5 = 0 \implies x = 5$$ $$x + 5 = 0 \implies x = -5$$ 7. **Check for restrictions:** Since $x = 5$ makes the denominator zero, it is not a valid solution. 8. **Final solution:** $$x = -5$$