adding and subtracting ratiional expressions

Front

What is a rational expression?

Back

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

Front

How do you find the least common denominator (LCD) of rational expressions?

Back

To find the LCD, factor each denominator and take the highest power of each factor present in any of the denominators.

Front

What is the least common denominator of \( \frac{1}{6} \) and \( \frac{1}{3} \)?

Back

The least common denominator is 6.

Front

What is the first step in adding rational expressions?

Back

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

Front

How do you add \( \frac{1}{x+3} + \frac{1}{x-7} \)?

Back

Find the LCD, which is \( (x+3)(x-7) \), then rewrite each fraction with the LCD and combine.

Front

What is the formula for adding two fractions \( \frac{a}{b} + \frac{c}{d} \)?

Back

The formula is \( \frac{ad + bc}{bd} \).

Front

What is the common denominator when adding \( \frac{1}{x+3} + \frac{1}{x-7} \)?

Back

The common denominator is \( (x+3)(x-7) \).

Front

What is the result of \( \frac{2}{3} + \frac{1}{6} \)?

Back

The result is \( \frac{5}{6} \).

Front

How do you subtract rational expressions?

Back

Similar to addition, find a common denominator, rewrite the fractions, and then subtract the numerators.

Front

What is the result of \( \frac{5}{x+2} - \frac{3}{x+2} \)?

Back

The result is \( \frac{2}{x+2} \).