Adding Rational Expressions

Front

What is a rational expression?

Back

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

Front

What is the first step in adding rational expressions?

Back

The first step is to find a common denominator for the fractions.

Front

Why do fractions need a common denominator to be added?

Back

Fractions must have a common denominator to ensure that the values being added are equivalent.

Front

What is the least common denominator (LCD)?

Back

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

Front

How do you find the least common denominator of two fractions?

Back

To find the least common denominator, list the multiples of each denominator and identify the smallest multiple that appears in both lists.

Front

What happens if the denominators of the fractions are already the same?

Back

If the denominators are the same, you can directly add the numerators and keep the common denominator.

Front

What is the process for adding two rational expressions with different denominators?

Back

1. Find the least common denominator. 2. Rewrite each fraction with the LCD. 3. Add the numerators and keep the LCD as the denominator.

Front

Can you simplify a rational expression after adding?

Back

Yes, after adding, you can simplify the resulting expression if possible by factoring and reducing.

Front

What is an example of adding two rational expressions?

Back

For example, to add 1/3 and 1/4, find the LCD (12), rewrite as 4/12 + 3/12 = 7/12.

Front

What is the importance of checking for common factors in the numerator and denominator?

Back

Checking for common factors is important to simplify the expression and ensure it is in its simplest form.