6.6 Rational equations

Ideas in this lesson

State restrictions and isolate

Identify denominator restrictions, clear a denominator and solve the resulting linear equation.

Clear denominators with an LCD

Multiply every term by the LCD, solve and substitute into the original equation.

Solve resulting quadratics

A rational equation may become quadratic after clearing denominators. Find every candidate and check each against the original restrictions.

Reject extraneous solutions

A candidate that makes an original denominator zero cannot solve the original equation.

Choose and justify cross multiplication for a proportion, solve, and verify original restrictions

choose and justify cross multiplication for a proportion, solve, and verify original restrictions.

Distinguish identity, contradiction and exceptional-parameter cases, explaining solution sets on the original domain

distinguish identity, contradiction and exceptional-parameter cases, explaining solution sets on the original domain.

Solve by numerical tables and graph intersections, state tolerances and identify missed/interior/extraneous candidates

solve by numerical tables and graph intersections, state tolerances and identify missed/interior/extraneous candidates.

Invert a given contextual rational model to find a target input/year/quantity, retaining its valid interval and units

invert a given contextual rational model to find a target input/year/quantity, retaining its valid interval and units.

Diagnose invalid first steps, explain equivalence on the restricted domain and choose an efficient solving method

diagnose invalid first steps, explain equivalence on the restricted domain and choose an efficient solving method.