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

What is the common denominator of \( \frac{2x}{x+1} \) and \( \frac{1}{x^2-1} \)?

Back

The common denominator is \( (x+1)(x-1) \).

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.

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

Simplify the expression \( \frac{6x}{20xy} \).

Back

The simplified expression is \( \frac{3}{10y} \).

Front

What is the common denominator of \( \frac{1}{x+2} \) and \( \frac{1}{x-2} \)?

Back

The common denominator is \( (x+2)(x-2) \).

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 the result of simplifying \( \frac{12n^2 + 28n + 4}{(2n-5)(n+2)} \)?

Back

The result is \( \frac{12n^2 - 28n + 4}{(2n-5)(n+2)} \).

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents.

Front

What is the difference between adding and subtracting rational expressions?

Back

Adding involves combining the numerators over a common denominator, while subtracting involves taking the difference of the numerators.