What is the significance of factoring in rational expressions?

Factoring is crucial in simplifying, adding, subtracting, and dividing rational expressions.

What is a hole in a rational expression?

A hole occurs in a rational expression at values that make both the numerator and denominator zero.

What is the vertical asymptote of a rational expression?

The vertical asymptote occurs at values that make the denominator zero but not the numerator.

How do you determine the domain of a rational expression?

The domain is all real numbers except for values that make the denominator zero.

What is the process for simplifying $$\frac{x^2+6x-7}{x^2-49}$$ ?

Factor to get $$\frac{(x+7)(x-1)}{(x+7)(x-7)}$$ , then cancel $$(x+7)$$ to simplify to $$\frac{x-1}{x-7}$$ .

What is the process for multiplying $$\frac{4}{x+2}$$ and $$\frac{x+3}{4}$$ ?

Multiply to get $$\frac{4(x+3)}{4(x+2)}$$ , then simplify to $$\frac{x+3}{x+2}$$ .

What is the result of dividing $$\frac{x^2-1}{x+1}$$ by $$\frac{x-1}{x^2}$$ ?

Multiply by the reciprocal to get $$\frac{x^2-1}{x+1} \cdot \frac{x^2}{x-1}$$ , then simplify to $$\frac{x(x+1)}{x+1}$$ , resulting in $$x$$ .

What is the result of multiplying $$\frac{x+2}{4}$$ and $$\frac{4(x+1)}{x+3}$$ ?

Multiply to get $$\frac{(x+2)(4)(x+1)}{4(x+3)}$$ , then simplify to $$\frac{(x+2)(x+1)}{(x+3)}$$ .

Rational Expressions

Flashcard

•

Mathematics

•

9th - 12th Grade

•

Hard

•

CCSS

HSA.APR.D.6, HSA.APR.D.7, HSF-IF.C.7D

Standards-aligned

Wayground Content

FREE Resource

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15 questions

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FLASHCARD QUESTION

Front

What is a rational expression?

Back

A rational expression is a fraction where the numerator and the denominator are both polynomials.

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

FLASHCARD QUESTION

Front

What is the first step in dividing rational expressions?

Back

The first step is to multiply by the reciprocal of the divisor.

Tags

CCSS.HSA.APR.D.6

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

FLASHCARD QUESTION

Front

What is the formula for adding rational expressions with different denominators?

Back

To add rational expressions with different denominators, find a common denominator, rewrite each expression, and then combine the numerators.

Tags

CCSS.HSA.APR.D.7

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

FLASHCARD QUESTION

Front

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

Back

The least common denominator is found by determining the least common multiple of the denominators.

Tags

CCSS.HSA.APR.D.7

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