Rational Equations Techniques

Questions and Answers

What is a rational equation?

An equation that cannot be solved

An equation that only uses integers

An equation with only whole numbers

An equation in which one or more terms is a fractional one (correct)

What is the first step in solving rational equations?

State the restrictions

What must be done to clear an equation of fractions?

Multiply both sides by the LCD of all rational expressions

When solving a rational equation, you should not check the proposed solutions against the restrictions on the variable.

False Signup and view all the answers

What is the method to solve a rational equation?

Multiply the denominators to the numerators to cancel the denominators Signup and view all the answers

What do you use when adding or subtracting rational equations?

The LCD Signup and view all the answers

What are you doing when you add or subtract rational equations with an equal sign?

Solving for the variable x Signup and view all the answers

Study Notes

Rational Equations

A rational equation features one or more fractional terms.
The primary goal when solving is to eliminate the denominators within the equation.

Steps for Solving Rational Equations

Begin by establishing any restrictions on the variable, determining values that would make the denominator zero.
Multiply both sides of the equation by the Least Common Denominator (LCD) of all rational expressions to eliminate fractions.
Solve the simplified equation that results after clearing the denominators.
Check all proposed solutions against the restrictions to ensure validity, rejecting any that violate these conditions.

Techniques for Solving

When solving, focus on multiplying denominators by numerators to facilitate the cancellation of terms.
This method simplifies the equation without introducing extraneous solutions.

Adding & Subtracting Rational Equations

Use the Least Common Denominator (LCD) when adding or subtracting rational expressions to combine them properly.
Ensure that the resulting expression maintains equivalent values in the context of the equations.

Solving for Variables in Rational Equations

When presented with an equal sign during addition or subtraction of rational equations, the objective shifts to solving for the variable, such as ( x ).
Follow the same principles of clearing fractions and establishing valid solutions.

Description

This quiz covers the essential techniques for solving rational equations. Learn how to eliminate denominators, apply the Least Common Denominator (LCD), and verify solutions against restrictions. Test your understanding of adding and subtracting rational expressions.