Add and Subtract 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 two rational expressions?

Back

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

Front

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

Back

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

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 in the numerator and denominator.

Front

What is the difference between adding and subtracting rational expressions?

Back

When adding, you combine the numerators over the common denominator; when subtracting, you subtract the numerators over the common denominator.

Front

What is the formula for adding two rational expressions?

Back

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

Front

What is the formula for subtracting two rational expressions?

Back

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

Front

What is a polynomial?

Back

A polynomial is an expression consisting of variables raised to non-negative integer powers and coefficients.

Front

What is the significance of factoring in rational expressions?

Back

Factoring is important because it helps to simplify expressions and find common denominators.

Front

What is the relationship between rational expressions and their graphs?

Back

The graph of a rational expression can have vertical asymptotes where the denominator is zero and horizontal asymptotes based on the degrees of the numerator and denominator.