Solving Rational Equations

Front

What is a rational equation?

Back

A rational equation is an equation that involves at least one rational expression, which is a fraction where the numerator and/or denominator are polynomials.

Front

How do you solve a rational equation?

Back

To solve a rational equation, find a common denominator, eliminate the fractions by multiplying both sides by that denominator, and then solve the resulting polynomial equation.

Front

What is the importance of checking for extraneous solutions in rational equations?

Back

Checking for extraneous solutions is important because multiplying by a variable can introduce solutions that do not satisfy the original equation.

Front

Back

The first step is to factor the denominators and find a common denominator to eliminate the fractions.

Front

Back

x = 0.

Front

What does it mean to find a common denominator?

Back

Finding a common denominator means identifying a shared multiple of the denominators in the equation to combine the fractions into a single fraction.

Front

Back

x = -\frac{13}{4}.

Front

What is an extraneous solution?

Back

An extraneous solution is a solution that emerges from the process of solving an equation but does not satisfy the original equation.

Front

Back

x = 6.

Front

What is the significance of the denominator in a rational equation?

Back

The denominator cannot be zero, as this would make the expression undefined.