Solving 2/(x + 1) + 3/(x - 2) = 1

Algebra 2 · Axiom Academy

Solve a rational equation with the LCD method, then check each candidate solution for extraneous roots. Solve for all real values of x using the LCD method — then check every candidate solution for extraneous roots. Excellent work! You solved a rational equation with the LCD method and confirmed both candidate solutions are valid. Remember: Find the LCD first: identify every denominator, then multiply by their least common multiple to clear all the fractions. Note domain restrictions BEFORE solving: any value that makes a denominator zero — here, and — is automatically excluded. Not every quadratic factors nicely: when it doesn't, the quadratic formula always finds the exact solutions. Always check every candidate in the ORIGINAL equation: both and check out exactly and are valid — neither matches a restricted value. If a candidate solution DOES equal a restricted value, it's extraneous — you must exclude it from your final answer, even though it came from valid algebra.

This is the written version of the interactive lesson above. See the full Algebra 2 course.