6.1 Simplifying rational expressions

Ideas in this lesson

Identify restrictions

Find excluded inputs from every original denominator before simplifying.

Factor completely

Factor the numerator and denominator before identifying common factors. Terms joined by addition cannot be canceled separately.

Cancel common factors

Divide numerator and denominator by a common nonzero factor. Retain restrictions from the original expression.

Retain the original domain

A canceled denominator factor still excludes its zero from the original domain.

Simplify multivariable monomial expressions and state relevant nonzero restrictions

simplify multivariable monomial expressions and state relevant nonzero restrictions.

Diagnose illegal cancellation and explain/correct the error with a valid rewrite or counterexample

diagnose illegal cancellation and explain/correct the error with a valid rewrite or counterexample.

Verify a simplification with numerical tables and graphs, explicitly identifying excluded inputs and holes hidden by a coarse graph

verify a simplification with numerical tables and graphs, explicitly identifying excluded inputs and holes hidden by a coarse graph.

Build and simplify geometric ratios (perimeter/area, surface area/volume, volume ratios), compare designs and interpret scaling with positive dimensions

build and simplify geometric ratios (perimeter/area, surface area/volume, volume ratios), compare designs and interpret scaling with positive dimensions.