Adding/Subtracting Rational 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 add rational expressions with the same denominator?

Back

To add rational expressions with the same denominator, combine the numerators and keep the denominator the same: \( \frac{a}{c} + \frac{b}{c} = \frac{a + b}{c} \).

Front

What is the first step in adding rational expressions with different denominators?

Back

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

Front

What is a common denominator?

Back

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

Front

How do you subtract rational expressions with the same denominator?

Back

To subtract rational expressions with the same denominator, subtract the numerators and keep the denominator the same: \( \frac{a}{c} - \frac{b}{c} = \frac{a - b}{c} \).

Front

What is the process to find a common denominator for \( \frac{1}{x} \) and \( \frac{1}{x+1} \)?

Back

The common denominator is \( x(x+1) \).

Front

How do you add \( \frac{2}{x} + \frac{3}{x+1} \)?

Back

Convert to a common denominator: \( \frac{2(x+1)}{x(x+1)} + \frac{3x}{x(x+1)} = \frac{2x + 2 + 3x}{x(x+1)} = \frac{5x + 2}{x(x+1)} \).

Front

What is the formula for subtracting rational expressions?

Back

The formula is: \( \frac{a}{c} - \frac{b}{d} = \frac{ad - bc}{cd} \) when the denominators are different.

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?

Back

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