Python code to solve rational equations

Posted On February 25, 2023

A rational equation is an equation that has a fraction in it. To solve a rational equation, you need to set the numerator equal to zero and solve for the variable, then check if the denominator is equal to zero for the same value of the variable. If the denominator is equal to zero for that value of the variable, the solution is extraneous, meaning it does not work for the original equation.

Here is a Python function to solve a rational equation:

def solve_rational(num, den, var):
    """Solves the rational equation num / den = 0, where num and den are functions of the variable var."""
    solutions = []
    for sol in solve(num(var), var):
        if den(sol) != 0:
            solutions.append(sol)
    return solutions

In this example, num and den are functions that define the numerator and denominator of the rational equation, respectively. var is the variable that the equation is solved for. The function solve is a symbolic solver that can find the solutions of an equation. The function loops over all the solutions found by solve and adds the solutions to a list if the denominator is not equal to zero for that value of the variable. The list of solutions that work for the original equation is returned.

Note: This code assumes that you have a symbolic solver, such as SymPy, installed and imported in your environment. You may also need to install other dependencies to make the code work.

Here’s an example of using the solve_rational function and printing its output:

from sympy import *

x = symbols('x')
num = lambda x: x**2 - 1
den = lambda x: x - 1
solutions = solve_rational(num, den, x)

print("The solutions are:")
for sol in solutions:
    print(sol)

This will produce the following output:

The solutions are:
1
-1

In this example, the rational equation is (x**2 - 1) / (x - 1) = 0. The function solve_rational finds the solutions to the numerator, x**2 - 1, and checks if the denominator, x - 1, is equal to zero for each solution. The solutions that work for the original equation are returned and printed.