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

The result is $$\frac{x+2}{4(x+1)}$$ after simplification.

What is the result of multiplying $$\frac{(x+9)(x+8)}{8}$$ and $$\frac{(x-1)}{(x+8)(x-1)}$$ ?

The result is $$\frac{x+9}{8}$$ after simplification.

What is the result of multiplying $$\frac{x^2+x-30}{x-7}$$ and $$\frac{2x-14}{x+6}$$ ?

The result is $$2(x-5)$$ after simplification.

What is the result of multiplying $$\frac{x^2-x-6}{x-3}$$ and $$\frac{x+9}{x+2}$$ ?

The result is $$x+9$$ after simplification.

What is the result of multiplying $$\frac{4x+8}{x^2-25}$$ and $$\frac{x-5}{5x+10}$$ ?

The result is $$\frac{4}{5(x+5)}$$ after simplification.

What is a common mistake when multiplying rational expressions?

A common mistake is forgetting to factor the expressions before multiplying, which can lead to incorrect simplification.

What is the importance of checking for restrictions in rational expressions?

It's important to check for restrictions to avoid division by zero, which is undefined.

What does it mean to have a common factor in rational expressions?

A common factor is a term that appears in both the numerator and the denominator, which can be canceled out during simplification.

How can you verify your answer after multiplying rational expressions?

You can verify your answer by substituting a value for the variable and checking if both the original and simplified expressions yield the same result.

Multiplying 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 both the numerator and the denominator are polynomials.

2.

FLASHCARD QUESTION

Front

How do you multiply two rational expressions?

Back

To multiply two rational expressions, multiply the numerators together and the denominators together, then simplify if possible.

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

What does it mean to simplify a rational expression?

Back

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

5.

FLASHCARD QUESTION

Front

What is the formula for multiplying two fractions?

Back

6.

FLASHCARD QUESTION

Front

What is the significance of factoring in multiplying rational expressions?

Back

Factoring helps identify and cancel common factors, making it easier to simplify the expression.

7.

FLASHCARD QUESTION

Front

Back

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