How do you find the common denominator for $$\frac{4}{x+8} + \frac{3}{x-5}$$ ?

The common denominator is $$(x+8)(x-5)$$ .

What is the result of simplifying $$\frac{6}{x-3} + \frac{4x}{x-1}$$ ?

The result is $$\frac{4x^2 - 6x - 6}{x^2 - 4x + 3}$$ .

What is the common denominator for $$\frac{2x}{x-5} + \frac{3x+2}{x+1}$$ ?

The common denominator is $$(x-5)(x+1)$$ .

How do you simplify $$\frac{2x}{x-5} + \frac{3x+2}{x+1}$$ ?

Combine the fractions over the common denominator and simplify the numerator.

What is the simplified form of $$\frac{2x}{x-5} + \frac{3x+2}{x+1}$$ ?

The simplified form is $$\frac{5x^2 - 11x - 10}{(x-5)(x+1)}$$ .

What is a polynomial?

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

What does it mean to simplify a rational expression?

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

What is the result of simplifying $$\frac{6x}{5x-4} + \frac{6}{x+6}$$ ?

The result is $$\frac{6x^2 + 66x - 24}{5x^2 + 26x - 24}$$ .

What is the importance of checking for restrictions in rational expressions?

Restrictions are important because they identify values that make the denominator zero, which are not allowed.

What is the simplified form of $$\frac{12n^2 - 28n + 4}{(2n-5)(n+2)}$$ ?

The simplified form is $$\frac{12n^2 - 28n + 4}{(2n-5)(n+2)}$$ , ensuring no further simplification is possible.

Adding and Subtracting 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 the numerator and the denominator are both polynomials.

2.

FLASHCARD QUESTION

Front

What is the first step in adding or subtracting rational expressions?

Back

The first step is to find a common denominator for the expressions.

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

What is the formula for adding two rational expressions?

Back

5.

FLASHCARD QUESTION

Front

Back

Find a common denominator, combine the numerators, and simplify the resulting expression.

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

What is the significance of factoring in adding rational expressions?

Back

Factoring helps to simplify the expressions and find common denominators more easily.

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