Determine the values of the variable that cannot possibly be solutions of each equation. Do not solve. See Examples 1 and 2. 5/(2x) - 2/x = 6

Verified step by step guidance

1. Identify the denominators in the equation: $2x$ and $x$.
2. Determine the values of $x$ that make the denominators equal to zero, as these will make the expression undefined.
3. Set each denominator equal to zero: $2x=0$ and $x=0$.
4. Solve each equation for $x$: $x=0$ for both equations.
5. Conclude that $x=0$ is the value that cannot be a solution, as it makes the denominators undefined.

Key Concepts

Undefined Values

In algebra, certain values can make an expression undefined, particularly when they result in division by zero. For example, in the equation 5/(2x) - 2/x, if x equals zero, both terms become undefined. Identifying these values is crucial for determining which cannot be solutions to the equation.

Rational Expressions

Rational expressions are fractions where the numerator and denominator are polynomials. In the given equation, the terms 5/(2x) and -2/x are rational expressions. Understanding how to manipulate and analyze these expressions helps in identifying restrictions on the variable that prevent valid solutions.

Domain of a Function

The domain of a function refers to the set of all possible input values (or x-values) that will not cause any undefined behavior in the function. For the equation provided, determining the domain involves finding values of x that do not lead to division by zero, thus clarifying which values are excluded from being solutions.