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What is the importance of the conjugate in rationalizing the denominator of a rational expression that has a radical expression in the denominator?
To eliminate the radical in the denominator.
What is an expression which contains polynomials in both the numerator and denominator?
rational expression
When can you simplify a fraction or a rational algebraic expression?
When the denominator is a factor of the numerator. If there is 2x in the numerator and denominator these terms cancel.
A rational expression is undefined whenever its denominator is zero?
False
When solving a rational equation why it is OK to remove the denominator by multiplying both sides by the LCD and why can you not do the same operation when simplifying a rational expression?
You can multiply both sides by the LCD because as a rule, you can do anything to one side of an equation as long as you do the same thing to the other side. But when you simplify a rational EXPRESSION, you don't have an EQUATION. So there is no other side. So you can't multiply both sides by anything. You can, however, multiply both the numerator and the denominator by the same term (except zero).
What fraction having rational expression in its numerator or denominator or both?
If you divide a rational expression by another rational expression, you will again get a rational expression.
How do you determine the values for which a rational expression is undefined?
A rational expression is not defined whenever the denominator of the expression equals zero. These will be the roots or zeros of the denominator.
What is the importance of the conjugate in rationalizing the denominator of a rational expression that has a radical expression in the denominator?
To eliminate the radical in the denominator.
An expression which contains polynomials in both the numerator and denominator?
rational expression
What is an expression which contains polynomials in both the numerator and denominator?
rational expression
How polynomial expression is a rational expression?
A polynomial expression is considered a rational expression when it is expressed as a fraction where both the numerator and the denominator are polynomials. For example, the expression ( \frac{x^2 + 3x + 2}{x - 1} ) is a rational expression because its numerator ( x^2 + 3x + 2 ) and denominator ( x - 1 ) are both polynomials. Rational expressions can be simplified, added, or multiplied, just like rational numbers, provided that the denominator is not zero.
To add two rational expressions that have the same deniminator you simply add the?
To add two rational expressions with the same denominator, you simply add the numerators together while keeping the denominator unchanged. The result is a new rational expression represented as (\frac{a + b}{c}), where (a) and (b) are the numerators of the original expressions, and (c) is the common denominator. Make sure to simplify the resulting expression if possible.
How do you write a rational number as a decimal?
You divide the numerator of the rational expression by its denominator.
What can the denominator of a rational expression never equal?
It cannot be zero.
A rational expression is undefined whenever its denominator is zero-?
True
Why must you always be mindful of the final value of the denominator in a rational expression?
The value of the denominator cannot be zero.
When is a racional expression undefined?
a rational expression is undefined when the denominator is 0 because we cannot dvide by 0.
