6.3 Adding and subtracting rational expressions

Ideas in this lesson

Common denominators

When denominators match, combine the numerators and keep the common denominator.

Least common denominators

The LCD contains each distinct irreducible factor to the greatest power appearing in any denominator.

Unlike denominators

Rewrite each fraction with the LCD, combine the numerators, factor and simplify where possible.

Subtract and simplify

Distribute a subtraction to the entire second numerator, then combine like terms and check for common factors.

Combine three or more rational/polynomial terms with an efficient common denominator

combine three or more rational/polynomial terms with an efficient common denominator.

Construct and simplify total travel-time expressions with unequal/with-and-against rates; interpret the domain

construct and simplify total travel-time expressions with unequal/with-and-against rates; interpret the domain.

Add a time-shifted rational model to an original model, state piecewise contextual applicability, graph the combined model and locate a numerical maximum

add a time-shifted rational model to an original model, state piecewise contextual applicability, graph the combined model and locate a numerical maximum. Use a safe fictional nonmedical setting, retaining the mathematical demand of book 8.5 exercise 44(a–d).

Explain or repair rational addition/subtraction reasoning and construct different expressions with a specified simplified result

explain or repair rational addition/subtraction reasoning and construct different expressions with a specified simplified result.