1. What is Rational Expression Simplification?

Rational expression simplification involves reducing complex algebraic fractions to their simplest form by factoring and canceling common factors in the numerator and denominator.

2. How Does the Calculator Work?

The calculator simplifies expressions of the form:

Where:

• \( x \) — Variable
• \( a \) — Coefficient of x in numerator
• \( b \) — Constant term in numerator
• \( c \) — Coefficient of x in denominator
• \( d \) — Constant term in denominator

Explanation: The calculator finds roots of both quadratic expressions and checks for common factors that can be canceled.

3. Importance of Simplifying Fractions

Details: Simplified forms are easier to work with in equations, graphing, and calculus operations like differentiation and integration.

4. Using the Calculator

Tips: Enter the coefficients a, b, c, and d from your quadratic expressions. The calculator will attempt to factor and simplify the expression if possible.

5. Frequently Asked Questions (FAQ)

Q1: What if the expression can't be simplified?
A: The calculator will indicate if the expression cannot be simplified further (when numerator and denominator have no common factors).

Q2: Does this work for higher degree polynomials?
A: This version only handles quadratic expressions. Higher degree polynomials require more advanced factoring techniques.

Q3: What about complex roots?
A: The calculator only simplifies when real roots exist (discriminant ≥ 0) and when there are common real roots.

Q4: Can I use decimal coefficients?
A: Yes, the calculator accepts decimal coefficients with up to 2 decimal places.

Q5: How accurate is the simplification?
A: The calculator uses a tolerance of 0.0001 when comparing roots to account for floating-point precision.