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

Verified step by step guidance

1. Identify the denominators in the equation: the denominators are \$2x\( and \)x$.
2. Set each denominator equal to zero to find values that make the denominators undefined: solve \$2x = 0\( and \)x = 0$.
3. From \$2x = 0\(, divide both sides by 2 to get \)x = 0$.
4. From \(x = 0\), we already have \(x = 0\) as a value that makes the denominator zero.
5. Conclude that \(x = 0\) is the value that cannot be a solution because it makes the denominators undefined.

Key Concepts

Domain Restrictions in Rational Expressions

Rational expressions involve variables in denominators, which cannot be zero because division by zero is undefined. Identifying values that make any denominator zero is essential to determine which variable values are excluded from the solution set.

Simplifying Rational Expressions

Before solving or analyzing rational equations, it is important to simplify expressions by finding common denominators or factoring. This helps in clearly identifying restrictions and understanding the structure of the equation.

Non-Solution Values vs. Solutions

Values that make denominators zero are not solutions and must be excluded from the solution set. Distinguishing between these excluded values and actual solutions is crucial, especially when the problem instructs not to solve but to identify impossible solutions.