Rational Equation Solver
Solve equations where one fraction is set equal to another fraction. Just enter the numerator, denominator and right hand side polynomial and let us handle the rest!
Equation Form
We are solving rational equations of the form:
Enter the polynomial expressions for p(x), q(x), and r(x) below.
Solutions for x:
Visual Representation
Understanding Rational Equations
A rational equation is an equation in which one or more terms are rational expressions. A rational expression is simply a fraction where the numerator and/or the denominator are polynomials. Solving a rational equation involves finding the values of the variable that make the equation true. This tool helps you solve equations of the form $$ \frac{p(x)}{q(x)} = r(x) $$, where p(x), q(x), and r(x) are polynomials. Solutions are found by identifying where the graphs of p(x)/q(x) and r(x) intersect, which are also the roots of the function f(x) = p(x)/q(x) - r(x).
- Polynomial: An expression consisting of variables and coefficients, involving only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
- Rational Expression: A fraction where the numerator and denominator are polynomials.
- Root Finding: The process of finding the values for which a function equals zero. In our case, we find roots of f(x) = p(x)/q(x) - r(x) to solve the equation.
For further learning, explore resources on polynomial equations and rational functions in algebra textbooks or online educational platforms like Khan Academy.