Tag Archives: rational functions

REX03 Ruling Out the Values of the Variable

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In the previous video, we have learned how to evaluate rational expressions. In this video, we are going to learn how to rule out the values of the variable in rational expressions. This concept is important because it is connected to the domain of rational functions  Watch the Tagalog math tutorial video above and then answer the exercises below. The complete video playlist of the Sipnayan tutorials on Rational Expressions can be found here.

Practice Exercise

Rule out the values of the variable of the following rational expressions.

1.) \dfrac{x + 4}{x}

2.) \dfrac{2x - 1}{x + 2}.

3.) \dfrac{x^2 - 1}{2x + 5}.

4.) \dfrac{x^2 + 2x}{x^2 - 9}.

5.) \dfrac{x - 9}{x^2 - 5x + 4}.

Answers

1. x \neq 0

2. x \neq -2

3. x \neq -\frac{5}{2}

4. x \neq 3, x \neq -3

5. x \neq 1, x \neq 4

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REX01 Introduction to Rational Expressions

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In this video, we learn the definition of rational numbers, rational expressions, and rational functions .  Watch the Tagalog math tutorial video above and then answer the exercises below. The complete video playlist of the Sipnayan tutorials on Rational Expressions can be found here.

Practice Exercise

True or False

1.)  The fraction \frac{\pi}{3} is a rational number.

2.) The fraction \frac{2x - 1}{5x + 1} is a rational expression.

3.) The fraction \frac{\sqrt{x} + 3}{x^2 + 3} is a rational expression.

4.) The function f(x) = \frac{1}{x} is a rational function.

5.) The fraction \frac{3}{8} is a rational number.

Answers

1.False. The numerator and denominator of a rational number must be integers.
2. True
3. False. \sqrt{x} + 3 is not a polynomial expression.
4. True
5. True

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