Adding and Subtracting 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

How do you add rational expressions with the same denominator?

Back

To add rational expressions with the same denominator, combine the numerators and keep the denominator the same.

Front

What is the first step in adding or subtracting rational expressions with different denominators?

Back

The first step is to find a common denominator.

Front

How do you simplify the expression (a + 2b) / 6b^2?

Back

The expression is already in its simplest form, as there are no common factors to reduce.

Front

What is the process for subtracting 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 the result of subtracting \( \frac{x^2-3}{2x+7} - \frac{2x-5}{2x+7} \)?

Back

The result is \( \frac{x^2-2x+2}{2x+7} \).

Front

What does it mean to simplify a rational expression?

Back

Simplifying a rational expression means reducing it to its lowest terms by factoring and canceling common factors.

Front

What is a common denominator?

Back

A common denominator is a shared multiple of the denominators of two or more fractions.

Front

How do you factor the expression x^2 - 3?

Back

The expression x^2 - 3 can be factored as (x - √3)(x + √3).

Front

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

Back

Factoring helps to identify common factors and simplify expressions, making it easier to add or subtract them.