Add and Subtract 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 different denominators?

Back

To add rational expressions with different denominators, find a common denominator, rewrite each expression, and then combine the numerators.

Front

What is the first step in subtracting rational expressions?

Back

The first step in subtracting rational expressions is to find a common denominator.

Front

What does it mean to simplify a rational expression?

Back

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

Front

What is the formula for adding two rational expressions?

Back

If \( \frac{a}{b} + \frac{c}{d} \), the formula is \( \frac{ad + bc}{bd} \).

Front

What is the formula for subtracting two rational expressions?

Back

If \( \frac{a}{b} - \frac{c}{d} \), the formula is \( \frac{ad - bc}{bd} \).

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 a polynomial?

Back

To factor a polynomial, find the greatest common factor (GCF) and use techniques like grouping or the quadratic formula.

Front

What is the importance of checking for extraneous solutions?

Back

Checking for extraneous solutions is important because some solutions may not satisfy the original equation, especially when dealing with rational expressions.

Front

What is the difference between adding and subtracting rational expressions?

Back

Adding rational expressions combines the numerators, while subtracting rational expressions involves subtracting the second numerator from the first.