1. What is Algebraic Fraction Equation?

The algebraic fraction equation \(\frac{a}{x} = \frac{b}{y} = c\) represents a proportional relationship between variables x and y through constants a, b, and c. It's commonly used in mathematics to solve for unknown variables in proportional relationships.

2. How Does the Calculator Work?

The calculator solves the equation:

Where:

• \( a \) — First coefficient (unitless)
• \( b \) — Second coefficient (unitless)
• \( c \) — Constant (unitless)
• \( x \) — First variable to solve for
• \( y \) — Second variable to solve for

Explanation: The calculator isolates either x or y by cross-multiplying and solving the resulting linear equation.

3. Importance of Solving Algebraic Fractions

Details: Solving algebraic fractions is fundamental in algebra and appears in various applications including physics, chemistry, and engineering problems involving proportional relationships.

4. Using the Calculator

Tips: Enter coefficients a and b, constant c (must be non-zero), and select which variable you want to solve for (x or y).

5. Frequently Asked Questions (FAQ)

Q1: What if the constant c is zero?
A: The equation becomes undefined when c = 0, as division by zero is not allowed in mathematics.

Q2: Can this calculator solve for both x and y simultaneously?
A: No, you need to solve for one variable at a time. The relationship between x and y would require additional information.

Q3: What if my coefficients are negative?
A: The calculator handles negative numbers correctly, following standard algebraic rules.

Q4: How precise are the results?
A: Results are rounded to 4 decimal places for readability, but maintain full precision in calculations.

Q5: Can this solve more complex fraction equations?
A: This calculator is designed specifically for equations of the form \(\frac{a}{x} = \frac{b}{y} = c\). More complex equations require different methods.