An Excluded Values Calculator helps you identify values that make a rational expression undefined. This occurs whenever the denominator equals zero. Use this tool to solve for $x$ in linear or quadratic denominators instantly.
Excluded Values Calculator
Enter the coefficients for the denominator: $ax^2 + bx + c$
Excluded Values Calculator Formula
To find the excluded values of a rational expression, you must set the denominator equal to zero and solve for the variable.
Source: Khan Academy – Rational Expressions
Variables:
- a (Coefficient of $x^2$): The number multiplying the squared term. Use 0 for linear equations.
- b (Coefficient of $x$): The number multiplying the $x$ term.
- c (Constant): The term without a variable.
Related Calculators:
- Domain and Range Finder
- Rational Expression Simplifier
- Quadratic Equation Solver
- Vertical Asymptote Calculator
What is an Excluded Values Calculator?
In mathematics, specifically algebra, an excluded value is a value of a variable that makes an expression undefined. For rational expressions (fractions where the numerator and denominator are polynomials), this happens when the denominator equals zero.
Even if a term in the numerator cancels out a term in the denominator during simplification, the value that originally made the denominator zero is still considered an excluded value because the original function is not defined at that point.
How to Calculate Excluded Values (Example)
Given the expression: $\frac{x+5}{x^2 – 5x + 6}$
- Identify the Denominator: $x^2 – 5x + 6$.
- Set it to Zero: $x^2 – 5x + 6 = 0$.
- Factor the Quadratic: $(x – 2)(x – 3) = 0$.
- Solve for x: $x = 2$ and $x = 3$.
- Result: The excluded values are 2 and 3.
Frequently Asked Questions (FAQ)
What happens at an excluded value? At these values, the graph of the function usually has a vertical asymptote or a hole (removable discontinuity).
Can there be no excluded values? Yes. If the denominator is a constant (like 5) or a quadratic that never equals zero (like $x^2 + 1$), there are no excluded values.
Do excluded values affect the domain? Yes, the domain of the function is all real numbers except the excluded values.
Why find excluded values first? It is critical to identify them before simplifying, as simplification might hide a value where the original function was undefined.