Solve Rational Equations Practice

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 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

What is the first step in solving a rational equation?

Back

The first step is to identify the least common denominator (LCD) of all the rational expressions in the equation.

Front

Why is it important to check for extraneous solutions?

Back

It is important to check for extraneous solutions because they can lead to incorrect conclusions about the solutions of the original equation.

Front

Solve for x: (x-2)/(x+3) = 1/2

Back

x = 1.

Front

Solve for y: (y+4)/(y-1) = 3/2

Back

y = 2.

Front

What does it mean to simplify a rational expression?

Back

To simplify a rational expression means to reduce it to its lowest terms by factoring and canceling common factors in the numerator and denominator.

Front

Solve for x: 2/(x-1) + 3/(x+1) = 1

Back

x = 0.

Front

What is the importance of finding a common denominator?

Back

Finding a common denominator allows you to combine fractions and eliminate them, making it easier to solve the equation.