Solve without squaring both sides: 5 - (2/x) = √(5 - 2/x).

Key Concepts

Rational Expressions

Rational expressions are fractions where the numerator and denominator are polynomials. Understanding how to manipulate these expressions is crucial for solving equations involving variables in the denominator, as seen in the given equation. Simplifying and finding common denominators can help isolate variables and solve for unknowns.

Square Roots

Square roots represent a value that, when multiplied by itself, gives the original number. In the context of the equation, recognizing how to work with square roots without squaring both sides is essential. This involves understanding properties of square roots, such as the fact that √a = b implies a = b², but also that both sides must remain valid under the operations performed.

Isolating Variables

Isolating variables is a fundamental algebraic technique used to solve equations. This involves rearranging the equation to get the variable of interest on one side. In the given problem, effectively isolating the term involving x will allow for a clearer path to finding the solution without squaring both sides, which can introduce extraneous solutions.