What must be excluded from the domain of the rational function $$\frac{x^2-64}{x^2-16}$$ ?

The rational function is undefined where the denominator is zero. Therefore, we must exclude the values that make $$x^2 - 16 = 0$$ , which are $$x = 4$$ and $$x = -4$$ .

Combine the fractions $$\frac{7x}{2} - \frac{3x}{8}$$ and express in fully reduced form.

The combined fraction is $$\frac{25x}{8}$$ .

Fully simplify the expression $$\frac{4x^2-40x+64}{x^3-6x^2} \times \frac{x^2-9x+18}{x^2-5x+6}$$ .

The simplified expression is $$\frac{4(x-8)}{x^2}$$ .

Find the sum of the rational expressions $$\frac{2}{x+3} + \frac{3}{x-1}$$ .

The sum is $$\frac{5x+7}{(x+3)(x-1)}$$ .

Divide the rational expressions $$\frac{x^2+3x-28}{2x^3} \div \frac{x^2-7x+12}{x-3}$$ .

The result of the division is $$\frac{x+7}{2x^3}$$ .

What is the process for adding rational expressions?

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

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

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

How do you determine the vertical asymptotes of a rational function?

Vertical asymptotes occur at the values of x that make the denominator zero, provided those values do not also make the numerator zero.

What is the difference between a removable and a non-removable discontinuity in rational functions?

A removable discontinuity occurs when a factor cancels out in the numerator and denominator, while a non-removable discontinuity occurs when the factor remains in the denominator.

What is the significance of the degree of the numerator and denominator in a rational function?

The degree of the numerator and denominator helps determine the end behavior of the function and the presence of horizontal asymptotes.

How do you simplify a complex fraction?

To simplify a complex fraction, multiply the numerator and denominator by the least common denominator of the fractions within the complex fraction.

What is the process for multiplying rational expressions?

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

What is the importance of factoring in working with rational expressions?

Factoring is crucial for simplifying expressions, finding common denominators, and identifying asymptotes and discontinuities.

How do you check if a rational expression is defined for a given value of x?

Substitute the value of x into the denominator; if the result is zero, the expression is undefined for that value.

Rational Expressions Flashcard Flashcards

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1.

FLASHCARD QUESTION

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2.

FLASHCARD QUESTION

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3.

FLASHCARD QUESTION

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4.

FLASHCARD QUESTION

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5.

FLASHCARD QUESTION

Front

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6.

FLASHCARD QUESTION

Front

What is a rational expression?

Back

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

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.

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