How do you factor the expression $$x^2 + 2x - 15$$ ?

The expression factors to $$(x + 5)(x - 3)$$ .

What is the first step in simplifying $$\frac{2n-3}{3-2n}$$ ?

Factor the numerator and denominator if possible, and notice that $$3 - 2n$$ can be rewritten as $$-(2n - 3)$$ .

What is the simplified form of $$\frac{8x^2}{12x^4}$$ ?

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

How do you simplify $$\frac{24x^2y}{32xy^3}$$ ?

Factor out the common terms to get $$\frac{3x}{4y^2}$$ .

What is the result of simplifying $$\frac{x^2 - 2x - 3}{x^2 - 5x - 6}$$ ?

The result is $$\frac{x - 3}{x - 6}$$ .

What is a polynomial?

A polynomial is an expression consisting of variables raised to whole number powers and coefficients.

What does it mean for a rational expression to be undefined?

A rational expression is undefined when its denominator equals zero.

What is the process of factoring a polynomial?

The process involves finding two or more expressions that multiply to give the original polynomial.

What is the significance of the degree of a polynomial in rational expressions?

The degree of a polynomial affects the behavior of the rational expression, including its asymptotes and intercepts.

How do you identify vertical asymptotes in rational expressions?

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

What is the simplified form of $$\frac{x^2 + 2x - 15}{x^2 - 10x + 21}$$ ?

The simplified form is $$\frac{x + 5}{x - 7}$$ .

What is the relationship between the roots of the numerator and the denominator in a rational expression?

The roots of the numerator indicate the x-intercepts, while the roots of the denominator indicate the vertical asymptotes.

Simplifying Rational Expressions Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a rational expression?

Back

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

2.

FLASHCARD QUESTION

Front

What does it mean to simplify a rational expression?

Back

To simplify a rational expression means to reduce it to its lowest terms by factoring and canceling common factors.

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

What is the importance of finding common factors in rational expressions?

Back

Finding common factors allows you to cancel them out, simplifying the expression.

7.

FLASHCARD QUESTION

Front

Back

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