1. What is This Complex Fraction?

The expression (150x + 110)/(15 + 125x) is a rational function (a fraction where both numerator and denominator are polynomials). Simplifying such expressions helps in understanding their behavior and solving equations.

2. How to Simplify the Fraction

The simplification process involves:

Steps:

1. Factor numerator and denominator
2. Find greatest common divisor (GCD)
3. Divide both numerator and denominator by GCD

3. Step-by-Step Simplification

Example: For x = 1:

• Numerator: 150(1) + 110 = 260
• Denominator: 15 + 125(1) = 140
• GCD of 260 and 140 is 20
• Simplified form: 260/140 = 13/7

4. Using the Calculator

Instructions: Enter any real number for x (except -0.12 which makes denominator zero) and click "Simplify" to see the reduced form and decimal value.

5. Frequently Asked Questions (FAQ)

Q1: What if denominator becomes zero?
A: The expression is undefined when 15 + 125x = 0 (x = -0.12). The calculator will show "Undefined".

Q2: Does this work for complex numbers?
A: This calculator handles real numbers only. For complex numbers, additional simplification steps are needed.

Q3: Can I see the factoring steps?
A: The calculator shows final simplified form. For step-by-step factoring, use a symbolic algebra system.

Q4: What's the most simplified form?
A: The fraction is fully simplified when numerator and denominator have no common factors other than 1.

Q5: Why is simplifying important?
A: Simplified forms are easier to work with in equations, graphing, and calculus operations.