How do you factor the expression $$x^2 - 9$$ ?

$$x^2 - 9$$ can be factored as $$(x - 3)(x + 3)$$ , which is a difference of squares.

What is the result of simplifying $$\frac{(3x-9)(x+6)}{(3x-9)(x-6)}$$ ?

The result is $$\frac{x+6}{x-6}$$ after canceling the common factor $$3x-9$$ .

What is the result of simplifying $$\frac{(x+2)(x-3)}{(x+2)(x+5)}$$ ?

The result is $$\frac{x-3}{x+5}$$ after canceling the common factor $$x+2$$ .

What is the result of simplifying $$\frac{(5x+10)(x-1)}{(5x+10)(x+1)}$$ ?

The result is $$\frac{x-1}{x+1}$$ after canceling the common factor $$5x+10$$ .

What is the result of simplifying $$\frac{(x^2-9)(x+4)}{(x^2-9)(x-4)}$$ ?

The result is $$\frac{x+4}{x-4}$$ after canceling the common factor $$x^2-9$$ .

What does it mean to cancel in a rational expression?

To cancel means to remove common factors from the numerator and denominator, simplifying the expression.

What is the simplified form of $$\frac{(x-1)(x+1)}{(x-1)(x-2)}$$ ?

The simplified form is $$\frac{x+1}{x-2}$$ after canceling the common factor $$x-1$$ .

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

Identifying common factors is crucial for simplifying the expression and finding equivalent forms.

What happens if there are no common factors in a rational expression?

If there are no common factors, the expression is already in its simplest form.

What is the result of simplifying $$\frac{(x^2-1)(x+3)}{(x^2-1)(x-3)}$$ ?

The result is $$\frac{x+3}{x-3}$$ after canceling the common factor $$x^2-1$$ .

What is the result of simplifying $$\frac{(2x+4)(x-5)}{(2x+4)(x+5)}$$ ?

The result is $$\frac{x-5}{x+5}$$ after canceling the common factor $$2x+4$$ .

What is the simplified form of $$\frac{(x^2-4)(x+1)}{(x^2-4)(x-1)}$$ ?

The simplified form is $$\frac{x+1}{x-1}$$ after canceling the common factor $$x^2-4$$ .

Simplifying Rational Expressions (already factored) 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 both the numerator and the denominator are polynomials.

2.

FLASHCARD QUESTION

Front

What does it mean to simplify a rational expression?

Back

Simplifying a rational expression means reducing it to its simplest form by canceling common factors in the numerator and denominator.

3.

FLASHCARD QUESTION

Front

What is the first step in simplifying a rational expression?

Back

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

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

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6.

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7.

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