Simplifying Rational Expressions

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What is a rational expression?

Back

A rational expression is a fraction where the numerator and the denominator are both polynomials.

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What does it mean to simplify a rational expression?

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

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What are excluded values in rational expressions?

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Excluded values are the values of the variable that make the denominator zero, as these values are not allowed in the expression.

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How do you find excluded values in a rational expression?

Back

Set the denominator equal to zero and solve for the variable.

Front

What is a vertical asymptote?

Back

A vertical asymptote is a line that a graph approaches but never touches, occurring at the excluded values of a rational expression.

Front

How do you determine the vertical asymptotes of a rational function?

Back

Vertical asymptotes can be found by identifying the values of x that make the denominator zero.

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Front

What is the first step in simplifying a complex rational expression?

Back

The first step is to factor the numerator and denominator where possible.

Front

What does it mean for two rational expressions to be equivalent?

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Two rational expressions are equivalent if they simplify to the same expression.

Front

What is the significance of common factors in rational expressions?

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Common factors can be canceled out to simplify the expression.