Adding and 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

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 first step in adding or subtracting rational expressions with different denominators?

Back

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

Front

How do you simplify the expression \( \frac{6x}{20xy} \)?

Back

The simplified form is \( \frac{3}{10y} \).

Front

What is the simplified form of \( \frac{n}{2m} \)?

Back

The expression is already in its simplest form.

Front

What is the result of \( \frac{x-5}{3x+4} - \frac{3x-5}{3x+4} \)?

Back

The result is \( \frac{-2x}{3x+4} \).

Front

How do you combine \( \frac{x^2-3}{2x+7} - \frac{2x-5}{2x+7} \)?

Back

Combine the numerators: \( \frac{x^2-3 - (2x-5)}{2x+7} = \frac{x^2-2x+2}{2x+7} \).

Front

What is the simplified form of \( \frac{2a + 4b}{12b^2} \)?

Back

The simplified form is \( \frac{a + 2b}{6b^2} \).

Front

What is the process to find a common denominator for \( \frac{a}{b} \) and \( \frac{c}{d} \)?

Back

The common denominator is the product of the two denominators: \( bd \).