What causes a solution to a rational equation to be an extraneous solution? When there is more than one solution, one of the solutions is extraneous. If a solution results in zero when substituted into the denominator of the equation, the solution is extraneous. If a solution results in a negative number when substituted into the denominator of the equation, the solution is extraneous. When a solution is a fraction, the solution is extraneous.
Solución de inteligencia artificial de Upstudy
Responder
Solución
Respondido por UpStudy AI y revisado por un tutor profesional


Extra Insights
Extraneous solutions often arise when we manipulate the equation, especially during the process of clearing denominators or squaring both sides. This can introduce solutions that don't actually satisfy the original equation. It’s like finding the elusive treasure only to discover it’s just fool’s gold! For example, consider the equation \( \frac{1}{x-2} = 0 \). If you multiply both sides by \( x-2 \), you might think the solution is \( x = 2 \). However, substituting back into the original equation leads to division by zero, making \( x = 2 \) an extraneous solution, proving that not every answer you find is a true gem!
