How do you find the least common denominator (LCD) of $$\frac{a}{b}$$ and $$\frac{c}{d}$$ ?

The LCD is the least common multiple (LCM) of the denominators, which is $$b \times d$$ if they are coprime.

What is the process to add $$\frac{a}{b}$$ and $$\frac{c}{d}$$ ?

Convert both fractions to have the same denominator, then add the numerators: $$\frac{a \times d + c \times b}{b \times d}$$ .

What is the result of $$\frac{5x}{10x} + \frac{15x}{10x}$$ ?

$$\frac{20x}{10x} = \frac{20}{10} = 2$$ .

How do you simplify $$\frac{7x}{x+1} + \frac{2}{x-3}$$ ?

Multiply each fraction by the necessary factor to have the same denominator: $$\frac{7x(x-3)}{(x+1)(x-3)} + \frac{2(x+1)}{(x-3)(x+1)}$$ .

What is the least common denominator of $$\frac{3x+2y}{3z} + \frac{15x+12y}{3z}$$ ?

The least common denominator is $$3z$$ .

What is the formula for the sum of two rational expressions with the same denominator?

If $$\frac{a}{c} + \frac{b}{c}$$ , then the sum is $$\frac{a+b}{c}$$ .

What is a polynomial?

A polynomial is an expression consisting of variables raised to non-negative integer 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 importance of factoring in adding and subtracting rational expressions?

Factoring helps to identify common factors that can be canceled, making the addition or subtraction simpler.

What is the result of $$\frac{7x}{x+1} + \frac{2}{x-3}$$ after finding the common denominator?

$$\frac{7x(x-3) + 2(x+1)}{(x+1)(x-3)}$$ .

What is the definition of a common denominator?

A common denominator is a shared multiple of the denominators of two or more fractions.

Adding and Subtracting Rational Expressions Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

Define 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 with different denominators?

Back

Find the least common denominator (LCD) of the expressions.

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

What is the next step after finding the LCD when adding rational expressions?

Back

Rewrite each expression with the LCD as the new denominator.

7.

FLASHCARD QUESTION

Front

Back

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