Given $$\frac{a}{m} + \frac{b}{n}$$ , how do you find the sum?

Find the LCD of $$m$$ and $$n$$ , rewrite each fraction with the LCD, then add the numerators.

How do you simplify the expression $$\frac{7}{n+9} + \frac{12}{4n+36}$$ ?

Factor the second denominator to get $$\frac{7}{n+9} + \frac{3}{n+9} = \frac{10}{n+9}$$ .

What is the result of $$\frac{a}{12b} - \frac{b}{8a}$$ ?

The result is $$\frac{2a^2 - 3b^2}{24ab}$$ .

How do you combine $$\frac{5x}{4} + \frac{x}{6}$$ ?

The result is $$\frac{17x}{12}$$ after finding the LCD and combining.

What is the simplified form of $$\frac{x}{2x-5} - \frac{4x+15}{4x^2-25}$$ ?

The simplified form is $$\frac{x+3}{2x+5}$$ .

How do you add $$\frac{r}{r^2-4} + \frac{1}{r^2-6r+8}$$ ?

The result is $$\frac{r-1}{(r+2)(r-4)}$$ after finding the LCD.

What is the importance of simplifying rational functions?

Simplifying rational functions makes them easier to work with and helps in solving equations or inequalities.

What does it mean for a rational function to be in simplest form?

A rational function is in simplest form when the numerator and denominator have no common factors other than 1.

How can you check if your answer for a rational function addition is correct?

You can check by substituting a value for the variable and ensuring both the original and simplified expressions yield the same result.

What is a common mistake when adding or subtracting rational functions?

A common mistake is failing to find a common denominator before combining the fractions.

8.2 Add/Subtract Rational functions Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

Define a rational function.

Back

A rational function is a function that can be expressed as the quotient of two polynomials, where the denominator is not zero.

2.

FLASHCARD QUESTION

Front

What is the least common denominator (LCD) and why is it important in adding or subtracting rational functions?

Back

The least common denominator (LCD) is the smallest multiple of the denominators of the rational functions involved. It is important because it allows us to combine the fractions into a single fraction.

3.

FLASHCARD QUESTION

Front

How do you find the sum of two rational functions?

Back

To find the sum of two rational functions, first find the LCD, rewrite each fraction with the LCD, then add the numerators and simplify.

4.

FLASHCARD QUESTION

Front

What is the process for subtracting rational functions?

Back

To subtract rational functions, find the LCD, rewrite each fraction with the LCD, subtract the numerators, and simplify the result.

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

What is the formula for the sum of two fractions with different denominators?

Back

7.

FLASHCARD QUESTION

Front

Back

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