What is the factored form of $$x^2 - 9$$ ?

The factored form is $$(x - 3)(x + 3)$$ .

What is the factored form of $$x^2 - 3x$$ ?

The factored form is $$x(x - 3)$$ .

After factoring, what is $$\frac{x^2 - 9}{x^2 - 3x}$$ simplified to?

It simplifies to $$\frac{(x - 3)(x + 3)}{x(x - 3)}$$ .

What can be cancelled in $$\frac{(x - 3)(x + 3)}{x(x - 3)}$$ ?

You can cancel $$(x - 3)$$ from the numerator and denominator.

What is the final simplified form of $$\frac{x^2 - 9}{x^2 - 3x}$$ ?

The final simplified form is $$\frac{x + 3}{x}$$ .

What is a common mistake when simplifying rational expressions?

A common mistake is cancelling terms that are not factors of both the numerator and denominator.

What is the importance of identifying restrictions in rational expressions?

Identifying restrictions is important because it helps to avoid division by zero, which is undefined.

What are the restrictions for the expression $$\frac{x + 6}{x - 5}$$ ?

The restriction is that $$x \neq 5$$ , as it would make the denominator zero.

How do you determine if a rational expression can be simplified?

Check if the numerator and denominator have any common factors that can be cancelled.

What is the simplified form of $$\frac{3x^2y^3}{9xy}$$ ?

The simplified form is $$\frac{x y^2}{3}$$ .

What does it mean if a rational expression cannot be simplified?

It means that the numerator and denominator do not have any common factors other than 1.

Simplifying Rational Expressions Flashcards

Student preview

15 questions

Show all answers

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 simplify a rational expression?

Back

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

Tags

CCSS.HSA.APR.D.6

3.

FLASHCARD QUESTION

Front

What does it mean to cancel in a rational expression?

Back

Cancelling means removing common factors from the numerator and denominator to simplify the expression.

Tags

CCSS.HSA.APR.D.6

4.

FLASHCARD QUESTION

Front

Back

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

Tags

CCSS.HSA.APR.D.6

5.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA.APR.C.4

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA.APR.D.6

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