Chapter 3: Operations with 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 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 the first step in simplifying a rational expression?

Back

The first step is to factor both the numerator and the denominator completely.

Front

What does it mean to simplify a rational expression?

Back

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

Front

What is the formula for dividing rational expressions?

Back

To divide rational expressions, multiply the first expression by the reciprocal of the second expression.

Front

What is a common denominator?

Back

A common denominator is a shared multiple of the denominators of two or more fractions, allowing them to be combined.

Front

What is the process of finding a common denominator?

Back

To find a common denominator, identify the least common multiple (LCM) of the denominators.

Front

What is the significance of factoring in rational expressions?

Back

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

Front

What is the result of subtracting (2/x) - (1/x)?

Back

The result is (1/x).

Front

How do you simplify (x^2 - 1)/(x + 1)?

Back

Factor the numerator to get (x - 1)(x + 1)/(x + 1) and then cancel (x + 1) to simplify to (x - 1).