What is the significance of excluding values in rational expressions?

Excluding values is important because they make the denominator zero, which is undefined in mathematics.

How do you simplify $$\frac{k^2+12k+32}{k^2+13k+40} \times \frac{k^2+5k}{k^2+6k+8}$$ ?

Factor each expression: $$\frac{(k+4)(k+8)}{(k+5)(k+8)} \times \frac{k(k+5)}{(k+2)(k+4)}$$ , then cancel common factors to get $$\frac{k}{k+2}$$ .

What is the result of $$\frac{6}{y-5} - \frac{y+5}{y^2-25}$$ ?

First, factor the denominator: $$y^2-25 = (y-5)(y+5)$$ . Then find a common denominator and simplify to get $$\frac{5}{y-5}$$ .

What does it mean to 'factor' a polynomial?

Factoring a polynomial means expressing it as a product of its factors, which are polynomials of lower degrees.

What is a common mistake when simplifying rational expressions?

A common mistake is to cancel terms that are not factors of the numerator and denominator.

What is the importance of checking for extraneous solutions in rational expressions?

Checking for extraneous solutions is important because some solutions may make the original expression undefined.

How do you add $$\frac{a}{b} + \frac{c}{d}$$ ?

To add, find a common denominator, which is $$bd$$ , then rewrite each fraction: $$\frac{ad + bc}{bd}$$ .

What is the process for solving rational equations?

To solve rational equations, first find a common denominator, eliminate the denominators, and then solve the resulting polynomial equation.

Operations with 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.

Tags

CCSS.HSA.APR.D.7

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 is the first step in adding or subtracting rational expressions?

Back

The first step is to find a common denominator.

Tags

CCSS.HSA.APR.D.7

4.

FLASHCARD QUESTION

Front

What is the formula for multiplying two rational expressions?

Back

Tags

CCSS.HSA.APR.D.7

5.

FLASHCARD QUESTION

Front

What is the formula for dividing two rational expressions?

Back

Tags

CCSS.HSA.APR.D.6

6.

FLASHCARD QUESTION

Front

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

Back

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

Tags

CCSS.HSA.APR.D.6

7.

FLASHCARD QUESTION

Front

How do you find the least common denominator (LCD) of two rational expressions?

Back

To find the LCD, factor each denominator and take the highest power of each factor that appears.

Tags

CCSS.HSA.APR.D.7

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