Adding and Subtracting Rational Functions

Front

What is a rational function?

Back

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

Front

How do you add rational functions with different denominators?

Back

To add rational functions with different denominators, find a common denominator, rewrite each function with that denominator, and then combine the numerators.

Front

What is the first step in subtracting rational functions?

Back

The first step in subtracting rational functions is to find a common denominator for both functions.

Front

What is a common denominator?

Back

A common denominator is a shared multiple of the denominators of two or more fractions, allowing them to be combined.

Front

How do you simplify a rational function?

Back

To simplify a rational function, factor both the numerator and the denominator and then cancel any common factors.

Front

What does it mean to find the least common denominator (LCD)?

Back

The least common denominator (LCD) is the smallest multiple that is common to the denominators of two or more fractions.

Front

What is the process of combining rational functions?

Back

The process involves finding a common denominator, rewriting each function, and then adding or subtracting the numerators.

Front

What is the importance of checking for restrictions in rational functions?

Back

Checking for restrictions is important because it identifies values that make the denominator zero, which are not allowed in rational functions.

Front

How do you determine the domain of a rational function?

Back

The domain of a rational function is determined by identifying all real numbers except those that make the denominator zero.

Front

What is the formula for adding two rational functions?

Back

If f(x) = a(x)/b(x) and g(x) = c(x)/d(x), then f(x) + g(x) = (a(x)d(x) + c(x)b(x)) / (b(x)d(x)).