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 denominator are polynomials.

Front

What does it mean to solve a rational equation?

Back

To solve a rational equation means to find the value(s) of the variable that make the equation true.

Front

What is cross-multiplication?

Back

Cross-multiplication is a method used to solve equations of the form a/b = c/d by multiplying the numerator of one fraction by the denominator of the other.

Front

How do you check if a solution is valid in a rational equation?

Back

To check if a solution is valid, substitute the solution back into the original equation and ensure that it does not make any denominator equal to zero.

Front

What is the first step in solving a rational equation?

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

Front

What is a common denominator?

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A common denominator is a shared multiple of the denominators of two or more fractions, used to combine or compare the fractions.

Front

What happens if you multiply both sides of a rational equation by the common denominator?

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Multiplying both sides by the common denominator eliminates the fractions, simplifying the equation.

Front

What is an extraneous solution?

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

Front

How do you isolate the variable in a rational equation?

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To isolate the variable, manipulate the equation using algebraic operations to get the variable on one side and constants on the other.

Front

What is the importance of factoring in solving rational equations?

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Factoring can simplify the equation and help identify potential solutions and restrictions.