Solving Rational Functions (6.3.1)

Front

Define a rational function.

Back

A rational function is a function that can be expressed as the quotient of two polynomials, where the denominator is not zero.

Front

What is the domain of a rational function?

Back

The domain of a rational function is all real numbers except where the denominator equals zero.

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Back

x = 5, x = 3

Front

What is the first step in solving a rational equation?

Back

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

Front

Back

x = -3

Front

What does it mean if a rational equation has no solution?

Back

It means that the equation leads to a contradiction, often due to division by zero.

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Back

No Solution

Front

What is a common method for solving rational equations?

Back

A common method is to find a common denominator and eliminate the fractions.

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Back

x = 0, 4

Front

What is the significance of finding the least common denominator (LCD) in rational functions?

Back

The LCD allows you to combine fractions and simplify the equation.