Use the quotient rule to simplify the expressions in Exercises 23–32. Assume that x > 0. √48x³/√3x

The quotient rule is a fundamental principle in calculus used to differentiate functions that are expressed as the ratio of two other functions. It states that if you have a function f(x) = g(x)/h(x), the derivative f'(x) can be found using the formula f'(x) = (g'(x)h(x) - g(x)h'(x)) / (h(x))^2. Understanding this rule is essential for simplifying expressions involving division.

Radical expressions involve roots, such as square roots or cube roots, and can often be simplified by applying properties of exponents. For example, √a = a^(1/2) and √(a/b) = √a/√b. Recognizing how to manipulate these expressions is crucial for simplifying the given expression involving square roots.

Simplifying expressions involves reducing them to their most basic form, which can include combining like terms, factoring, and reducing fractions. In the context of the given expression, this means applying the properties of radicals and the quotient rule to rewrite the expression in a simpler, more manageable form. Mastery of simplification techniques is vital for solving algebraic problems efficiently.