Final answer:
The question pertains to simplifying an algebraic expression involving square roots and falls under the high school mathematics category. It requires understanding of rational functions and various algebraic techniques such as factoring, rationalizing denominators, and applying the quadratic formula.
Step-by-step explanation:
The student's question involves a function f(x) which is defined as the ratio of the square root of (x-6) to the square root of (x-4). This is a concept involving rational functions and the simplification of expressions involving square roots, which falls under the mathematics category. The student is presumably in high school, as the manipulation and understanding of such algebraic expressions are commonly taught at this level. When simplifying expressions involving square roots, the focus is to isolate variables and apply algebraic principles like factoring, expanding, or the use of the quadratic formula to solve equations.
To begin simplifying the expression presented, you would first ensure that the domain of the function allows for the square roots to be defined (i.e., x must be greater than or equal to 6). Afterward, if necessary, you could multiply the numerator and the denominator by the conjugate of the denominator to rationalize the denominator and simplify further, if possible.
Concepts such as factoring, squaring both sides of an equation to eliminate square roots, and solving quadratic equations using formulas are applicable to manipulating the given expression. Additionally, understanding the properties of exponents (such as the square root of a number being the same as raising that number to the power of 1/2) is vital for working with these types of algebraic functions.