The question addresses the simplification of rational expressions and the application of algebraic concepts such as factoring, use of quadratic formulas, and understanding of negative exponents.
The student's question involves simplifying and combining rational expressions, which entails factoring, finding common denominators, and performing arithmetic operations on fractions. A critical skill in this process is recognizing patterns, such as perfect squares, that can guide the simplification of expressions. For example, the expression (x² - 4)/(x - 2) can be simplified by factoring the numerator as the difference of squares: (x + 2)(x - 2)/(x - 2), which can then be reduced by canceling out the (x - 2) factors. The factoring, expansion, and use of quadratic formulas are also crucial when dealing with quadratic equations. Understanding negative exponents, such as seeing that x-n is equivalent to 1/xn, is also important in algebra.