Adding and Subtracting Rational Expressions

Front

What is a rational expression?

Back

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

Front

How do you find the common denominator of rational expressions?

Back

To find the common denominator, factor each denominator and take the highest power of each factor present in any of the denominators.

Front

What is the first step in adding rational expressions?

Back

The first step is to find a common denominator for the expressions being added.

Front

What does it mean to simplify a rational expression?

Back

Simplifying a rational expression means reducing it to its lowest terms by canceling out common factors in the numerator and denominator.

Front

What is the formula for adding two rational expressions?

Back

If a/b and c/d are two rational expressions, the sum is (ad + bc) / bd.

Front

What is the importance of factoring in adding and subtracting rational expressions?

Back

Factoring helps to identify common factors and find the least common denominator, which is essential for performing addition or subtraction.

Front

How do you subtract rational expressions?

Back

To subtract rational expressions, find a common denominator, rewrite each expression with that denominator, and then subtract the numerators.

Front

What is an example of a common denominator for (x+2) and (x-2)?

Back

The common denominator is (x+2)(x-2).

Front

What is the result of simplifying (2x^2 + 4x) / (2x)?

Back

The simplified expression is x + 2.

Front

What is the result of adding 1/(x+1) and 1/(x+2)?

Back

The result is (3 + x) / ((x+1)(x+2)).