Final answer:
The student's inquiry is related to simplifying algebraic expressions, which could require multiplying by the denominator, taking square roots, or using the quadratic equation. The precise operations are not given, but the general approach includes maintaining equality by performing the same operations on both sides of an equation.
Step-by-step explanation:
The student's question seems to involve simplifying an algebraic expression that includes square roots and fractions. Given the provided context, it appears that by manipulating the expression and applying certain algebraic principles - such as multiplying both sides by the denominator, using the concept of perfect squares, and applying the quadratic equation when necessary - one could simplify the expression or solve for a variable. The actual mathematical operation or simplification, however, is not provided in the context, so we can't solve this particular expression. Instead, we focus on the principles that can be applied to simplify or solve algebraic expressions.
If you encounter an algebraic expression with the same quantity in both the numerator and the denominator, it simplifies to 1. If you have a perfect square in an equation, taking the square root of both sides may help simplify it. And when you have a quadratic equation, you may need to drop insignificant terms or complete the square to find the value of the variable.
Remember, simplifying an expression or solving an equation requires a step-by-step approach, ensuring that whatever operation is done on one side of the equals sign is also done on the other side, maintaining the equality.