Rational Expressions Reference

Algebra 1 · Axiom Academy

FORMULA SHEET Rational Expressions Reference Operations, domain restrictions, solving, and applications — at a glance. Simplifying Rational Expressions Factor the numerator completely. Factor the denominator completely. State the domain restrictions. Operations with Rational Expressions Finding the LCD & Solving Equations Factor each denominator completely. Take the highest power of each factor. Multiply all factors together. Find the LCD of all denominators. Multiply both sides by the LCD. Solve the resulting polynomial equation. Check each solution in the original equation. Simplify the numerator to a single fraction. Simplify the denominator to a single fraction. Divide: multiply by the reciprocal. Find the LCD of every inner fraction. Multiply the whole expression by that LCD. Cancelling terms instead of factors — only factors cancel. Forgetting to state the domain restrictions. Not checking for extraneous solutions. Multiplying the denominators when adding (use the LCD instead). Losing a negative sign when subtracting numerators.

This is the written version of the interactive lesson above. See the full Algebra 1 course.