Adding and Subtracting 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 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 is to find a common denominator for the expressions being subtracted.

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 formula for factoring a quadratic expression?

Back

The formula for factoring a quadratic expression ax^2 + bx + c is to find two numbers that multiply to ac and add to b.

Front

How do you solve for x in a rational equation?

Back

To solve for x in a rational equation, first eliminate the denominators by multiplying both sides by the least common denominator (LCD), then solve the resulting equation.

Front

What is the least common denominator (LCD)?

Back

The least common denominator (LCD) is the smallest multiple that is common to all denominators in a set of fractions.

Front

What is the result of adding (x + 2)/(x - 3) and (x - 1)/(x + 4)?

Back

The result is ((x + 2)(x + 4) + (x - 1)(x - 3)) / ((x - 3)(x + 4)).

Front

What is the result of subtracting (2x)/(x + 1) from (3x)/(x - 1)?

Back

The result is ((3x)(x + 1) - (2x)(x - 1)) / ((x - 1)(x + 1)).

Front

What is a common mistake when adding rational expressions?

Back

A common mistake is to add the numerators directly without finding a common denominator.