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

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

What is the simplified form of $$\frac{12n^2 + 28n + 4}{(2n-5)(n+2)}$$ ?

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

What is the result of adding $$\frac{1}{3} + \frac{1}{6}$$ ?

The result is $$\frac{1}{2}$$ .

What is the formula for subtracting rational expressions?

To subtract rational expressions, find a common denominator, rewrite each expression with that denominator, and then subtract the numerators.

What is the common denominator of $$\frac{3}{x}$$ and $$\frac{4}{x^2}$$ ?

The common denominator is $$x^2$$ .

How do you simplify $$\frac{(x^2 - 1)(x + 2)}{(x - 1)(x + 1)}$$ ?

Factor the numerator and cancel common factors to simplify to $$\frac{(x + 2)(x - 1)}{(x + 1)}$$ .

What is the result of $$\frac{5x}{2} - \frac{3x}{4}$$ ?

The result is $$\frac{7x}{4}$$ .

What is the definition of a polynomial?

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

What is the process of factoring a polynomial?

Factoring a polynomial involves rewriting it as a product of its factors.

What is the significance of the degree of a polynomial?

The degree of a polynomial indicates the highest power of the variable in the expression and determines its behavior.

What is the result of simplifying $$\frac{-17x - 12y}{15x}$$ ?

The expression is already in its simplest form.

Adding and Subtracting Rational Expressions Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a rational expression?

Back

A rational expression is a fraction where the numerator and the denominator are both polynomials.

2.

FLASHCARD QUESTION

Front

How do you find a common denominator for rational expressions?

Back

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

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

What is the first step in adding rational expressions?

Back

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

5.

FLASHCARD QUESTION

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.

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

Back

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