4.2 Rational Expressions Operations

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 common denominator?

Back

The common denominator is the least common multiple (LCM) of the denominators of two or more fractions.

Front

How do you find the common denominator for \( \frac{4}{x+8} + \frac{3}{x-5} \)?

Back

The common denominator is \( (x+8)(x-5) \).

Front

What does it mean to simplify a rational expression?

Back

To simplify a rational expression means to reduce it to its simplest form by canceling common factors in the numerator and denominator.

Front

What is the first step in adding rational expressions?

Back

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

Front

How do you simplify \( \frac{2a + 4b}{12b^2} \)?

Back

Factor the numerator: \( \frac{2(a + 2b)}{12b^2} = \frac{a + 2b}{6b^2} \).

Front

What is the result of simplifying \( \frac{n}{4m} + \frac{n}{2m} \)?

Back

The result is \( \frac{3n}{4m} \) after finding a common denominator.

Front

What is the process for subtracting rational expressions?

Back

1. Find a common denominator. 2. Rewrite each fraction with the common denominator. 3. Subtract the numerators.

Front

What is the significance of factoring in rational expressions?

Back

Factoring helps to simplify expressions and find common factors that can be canceled.

Front

How do you simplify \( \frac{x-9}{x+9} \)?

Back

This expression is already in its simplest form.