What is the result of $$\frac{3(x-9)}{x^2-36} \times \frac{x^2-x-30}{x-9}$$ ?

The result is $$\frac{3(x-9)(x^2-x-30)}{(x^2-36)(x-9)}$$ after applying the KFC method.

What is the factored form of $$x^2-36$$ ?

The factored form of $$x^2-36$$ is $$(x-6)(x+6)$$ .

How do you factor the expression $$x^2+x-12$$ ?

The expression $$x^2+x-12$$ factors to $$(x+4)(x-3)$$ .

What is the simplified form of $$\frac{x^3+3x^2-18x}{x^2+x-12}$$ ?

The simplified form is $$\frac{x(x+6)}{(x+4)}$$ .

What is the result of dividing $$\frac{x^2+11x+24}{x^2+4x-32}$$ ?

The result is $$\frac{x+3}{x-4}$$ after factoring and simplifying.

What does it mean to cancel common factors in rational expressions?

Canceling common factors means removing the same factor from the numerator and denominator to simplify the expression.

What is the importance of factoring in multiplying and dividing rational expressions?

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

What is the difference between multiplying and dividing rational expressions?

In multiplication, you multiply numerators and denominators directly; in division, you multiply by the reciprocal of the divisor.

What is a polynomial?

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

Multiply and Divide 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.

Tags

CCSS.HSA.APR.D.7

2.

FLASHCARD QUESTION

Front

What does it mean to multiply rational expressions?

Back

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

Tags

CCSS.HSA.APR.D.7

3.

FLASHCARD QUESTION

Front

What is the reciprocal of a rational expression?

Back

Tags

CCSS.HSA.APR.D.6

4.

FLASHCARD QUESTION

Front

What is the KFC method in division of rational expressions?

Back

KFC stands for Keep, Flip, Change: Keep the first fraction, Flip the second fraction (take its reciprocal), and Change the division to multiplication.

Tags

CCSS.HSA.APR.D.6

5.

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

6.

FLASHCARD QUESTION

Front

What is the first step in dividing rational expressions?

Back

The first step is to multiply by the reciprocal of the second expression.

Tags

CCSS.HSA.APR.D.6

7.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA.APR.D.6

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