6.3 Rational Equations Review

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

What is the first step in solving a rational equation?

Back

The first step is to identify any restrictions on the variable that would make the denominator zero.

Front

How do you find the least common denominator (LCD) in rational equations?

Back

The least common denominator is found by determining the least common multiple of the denominators of all rational expressions in the equation.

Front

What does it mean to check for extraneous solutions?

Back

Checking for extraneous solutions means substituting the found solutions back into the original equation to ensure they do not make any denominator zero.

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Back

x = -4.5

Front

Back

x = \frac{4}{5}

Front

What is the significance of the variable in the denominator of a rational expression?

Back

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

Front

What is an example of a rational expression?

Back

Front

How do you solve a rational equation with multiple fractions?

Back

Multiply both sides of the equation by the least common denominator to eliminate the fractions.

Front

What is an extraneous solution?

Back

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