Solve The Following Rational Equation Calculator

How to Use This Calculator

This calculator helps you solve rational equations of the form:

(a/x) + (b/y) = c

To use the calculator:

The calculator will show you the step-by-step solution and any restrictions that must be considered.

A rational equation is an equation that contains at least one fraction where the numerator and denominator are polynomials. The most common form is:

(a/x) + (b/y) = c

To solve a rational equation, you need to eliminate the denominators by finding a common denominator and then solve for the variable.

First, identify the rational equation you need to solve. It should be in the form:

(a/x) + (b/y) = c

The common denominator for x and y is xy. Multiply every term by xy to eliminate the denominators:

xy*(a/x) + xy*(b/y) = xy*c

This simplifies to:

ay + bx = cxy

Rearrange the equation to solve for the variable. For example, if you're solving for x:

bx = cxy - ay x = (cxy - ay)/b

After solving, check if the solution makes any denominator zero. If it does, that value is not allowed and should be excluded.

When solving rational equations, it's easy to make these common mistakes:

Always double-check your work and verify that your solution doesn't make any denominator zero.

What is a rational equation?: A rational equation is an equation that contains at least one fraction where the numerator and denominator are polynomials.
How do I solve a rational equation?: To solve a rational equation, find a common denominator, eliminate the denominators, solve the resulting equation, and check for extraneous solutions.
What are extraneous solutions?: Extraneous solutions are solutions that emerge from the solving process but don't satisfy the original equation. They occur when you divide by a variable that equals zero.
Can I use this calculator for any rational equation?: This calculator is designed for equations of the form (a/x) + (b/y) = c. For more complex rational equations, you may need to solve them manually.