What are the factors of $$x^2-49$$ ?

$$(x-7)(x+7)$$ (difference of squares).

What is the simplified form of $$\frac{x^2+6x-7}{x^2-49}$$ ?

$$\frac{x-1}{x-7}$$ after canceling the common factor.

What is the result of multiplying $$\frac{x+2}{x-3}$$ and $$\frac{x-1}{x+4}$$ ?

$$\frac{(x+2)(x-1)}{(x-3)(x+4)}$$ .

What is the process to add or subtract rational expressions?

Find a common denominator, rewrite each expression, and then combine the numerators.

What is a common mistake when simplifying rational expressions?

Canceling terms that are not factors of both the numerator and denominator.

What is the simplified form of $$\frac{x^2+7x+10}{x^2-4}$$ ?

$$\frac{x+5}{x-2}$$ after factoring and canceling.

What does it mean for a rational expression to be undefined?

A rational expression is undefined when its denominator equals zero.

What are the restrictions on the variable in $$\frac{x^2+6x-7}{x^2-49}$$ ?

The variable x cannot be 7 or -7, as these values make the denominator zero.

What is the difference between a proper and improper rational expression?

A proper rational expression has a degree of the numerator less than the degree of the denominator; an improper one has a degree of the numerator greater than or equal to the denominator.

How can you check if your simplification of a rational expression is correct?

You can substitute values into the original and simplified expressions to see if they yield the same result.

Rational Expressions Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What is a rational expression?

Back

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

2.

FLASHCARD QUESTION

Front

How do you simplify a rational expression?

Back

To simplify a rational expression, factor both the numerator and the denominator and then cancel any common factors.

3.

FLASHCARD QUESTION

Front

Back

Factor both the numerator and the denominator.

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

What is the importance of identifying common factors in rational expressions?

Back

Identifying common factors allows you to simplify the expression, making calculations easier.

7.

FLASHCARD QUESTION

Front

How do you multiply two rational expressions?

Back

Multiply the numerators together and the denominators together, then simplify if possible.

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