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Questions and Answers
Which of the following is an algebraic expression?
Which of the following is an algebraic expression?
- 3x^2 - 2xy + c (correct)
- $\frac{1-x^2}{1+x^2}$
- $\frac{1}{x} + \frac{1}{y}$
- $\sqrt{3x-2xy+c}$
Which of the following is a rational expression?
Which of the following is a rational expression?
- $\frac{x+1}{x-1}$
- $\frac{3x-2xy+c}{y-1}$ (correct)
- $\frac{1-x^2}{1+x^2}$
- $\sqrt{3x-2xy+c}$
Which type of number is π?
Which type of number is π?
- Integer
- Transcendental (correct)
- Algebraic
- Rational
What does the expression $\frac{1-x^2}{1+x^2}$ represent?
What does the expression $\frac{1-x^2}{1+x^2}$ represent?
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What makes an expression a rational expression?
What makes an expression a rational expression?
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Study Notes
Algebraic and Rational Expressions
- An algebraic expression is an expression that contains variables, constants, and algebraic operations (addition, subtraction, multiplication, division, exponentiation, etc.)
- A rational expression is an expression of the form $\frac{p(x)}{q(x)}$, where $p(x)$ and $q(x)$ are polynomials and $q(x) \neq 0$.
Properties of π
- π (pi) is an irrational number, which means it cannot be expressed as a finite decimal or fraction.
Expression Analysis
- The expression $\frac{1-x^2}{1+x^2}$ represents a rational expression, as it is in the form of a fraction of polynomials.
Definition of Rational Expression
- A rational expression is an expression that can be written in the form $\frac{p(x)}{q(x)}$, where $p(x)$ and $q(x)$ are polynomials and $q(x) \neq 0$.
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