How do you simplify $$\frac{x^2-4x-12}{x+2}$$ ?

Factor the numerator: $$x^2-4x-12 = (x-6)(x+2)$$ . Then, cancel the common factor $$x+2$$ , resulting in $$x-6$$ .

What is the result of $$\frac{n+3}{8n^2+24n} \div \frac{n-1}{5n}$$ ?

Multiply by the reciprocal: $$\frac{n+3}{8n^2+24n} \times \frac{5n}{n-1} = \frac{5(n+3)}{8n(n+3)} = \frac{5}{8(n-1)}$$ after canceling $$n+3$$ .

How do you find the product of two rational expressions?

To find the product, multiply the numerators together and the denominators together. For example, $$\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}$$ .

What is the simplified product of $$\frac{x^2-11x+30}{x+1}$$ and $$\frac{x+1}{7x-42}$$ ?

Factor the first expression: $$x^2-11x+30 = (x-5)(x-6)$$ and the second: $$7x-42 = 7(x-6)$$ . The product simplifies to $$\frac{x-5}{7}$$ after canceling $$x+1$$ .

Define 'rational expression'.

A rational expression is a fraction where the numerator and the denominator are both polynomials. For example, $$\frac{p(x)}{q(x)}$$ where both $$p(x)$$ and $$q(x)$$ are polynomials.

What is the importance of identifying restrictions in rational expressions?

Identifying restrictions is important to avoid division by zero, which is undefined. For example, in $$\frac{1}{x-3}$$ , $$x \neq 3$$ .

How do you find the difference of $$\frac{9}{x-6}$$ and $$\frac{3}{x}$$ ?

Find a common denominator, which is $$x(x-6)$$ . Rewrite as $$\frac{9x - 3(x-6)}{x(x-6)} = \frac{6x + 18}{x(x-6)}$$ .

What is the result of adding $$\frac{6}{k-4}$$ and $$\frac{k+8}{k^2+2k-24}$$ ?

First, factor the second denominator: $$k^2+2k-24 = (k-4)(k+6)$$ . The sum is $$\frac{7k+44}{(k-4)(k+6)}$$ .

What is the simplified form of $$\frac{x^2-10x+31}{8x-41}$$ ?

This expression cannot be simplified further without specific values for $$x$$ .

AA C&C Final Exam Review Units 5 & 7 Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

Define the sum of rational expressions.

Back

Tags

CCSS.HSA.APR.D.7

2.

FLASHCARD QUESTION

Front

What is the process to simplify a rational expression?

Back

To simplify a rational expression, factor the numerator and denominator, cancel out any common factors, and rewrite the expression in its simplest form.

Tags

CCSS.HSA.APR.D.6

3.

FLASHCARD QUESTION

Front

How do you find the quotient of two rational expressions?

Back

Tags

CCSS.HSA.APR.D.6

4.

FLASHCARD QUESTION

Front

What is the difference of two rational expressions?

Back

Tags

CCSS.HSA.APR.D.7

5.

FLASHCARD QUESTION

Front

Define the term 'common denominator'.

Back

A common denominator is a shared multiple of the denominators of two or more fractions, allowing for addition or subtraction of the fractions.

6.

FLASHCARD QUESTION

Front

What is the significance of factoring in rational expressions?

Back

Factoring is crucial in simplifying rational expressions, as it allows for the cancellation of common factors in the numerator and denominator.

Tags

CCSS.HSA.APR.D.6

7.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA.APR.D.6

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