Add and subtract rational expressions

Front

What is a rational expression?

Back

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

Front

What is the first step to add or subtract rational expressions?

Back

The first step is to ensure that the expressions have a common denominator.

Front

How do you find a common denominator for two rational expressions?

Back

To find a common denominator, identify the least common multiple (LCM) of the denominators.

Front

What is the formula for adding two rational expressions?

Back

If \( \frac{a}{b} + \frac{c}{d} \), the formula is \( \frac{ad + bc}{bd} \) after finding a common denominator.

Front

What is the formula for subtracting two rational expressions?

Back

If \( \frac{a}{b} - \frac{c}{d} \), the formula is \( \frac{ad - bc}{bd} \) after finding a common denominator.

Front

What happens if the denominators are already the same when adding or subtracting?

Back

If the denominators are the same, you can directly add or subtract the numerators.

Front

What is the importance of simplifying rational expressions?

Back

Simplifying rational expressions makes them easier to work with and helps to identify any restrictions on the variable.

Front

What are restrictions in rational expressions?

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Restrictions are values that make the denominator zero, which are not allowed in rational expressions.

Front

How do you simplify a rational expression?

Back

To simplify, factor the numerator and denominator and cancel any common factors.

Front

What is an example of adding two rational expressions?

Back

Example: \( \frac{1}{2} + \frac{1}{3} = \frac{3}{6} + \frac{2}{6} = \frac{5}{6} \) after finding a common denominator.