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Rational Expressions and Functions — High School Algebra 2 practice questions

16 multiple-choice questions and 11 flashcards on Rational Expressions and Functions, about 11% of the High School Algebra 2 bank. Every one carries a written rationale.

Written and maintained by the CoStudy team · last updated 2026-10-12 · how we write and review questions

What this chapter covers

Rational Expressions and Functions is one of 9 chapters in CoStudy's High School Algebra 2 bank, and it holds 16 of the bank's 150 multiple-choice questions — roughly 11% of the total. That proportion is not arbitrary: chapters follow the certifying body's published exam outline, and the number of questions in each is set by that domain's published weight, so the share of your practice time this chapter takes matches the share of the real exam it accounts for.

Studying by chapter is worth doing once you have a diagnostic score. A single overall percentage tells you whether you are close; it does not tell you which domain is dragging. Working a weak chapter in isolation, and re-testing it in isolation, is the fastest way to move a score that has stalled — and it is why the mock exams in CoStudy report by domain rather than as one number.

Free Rational Expressions and Functions practice questions

1 questions drawn from this chapter, with the full rationale shown — the controlling principle behind the right answer, and why each wrong option tempts and fails.

Simplify (x² − 9)/(x² − x − 6).

  1. (x − 3)/(x − 2)
  2. (x + 3)/(x − 2)
  3. (x + 3)/(x + 2)
  4. 3/2

Answer: C — (x + 3)/(x + 2)

C) Correct — (x − 3)(x + 3) / ((x − 3)(x + 2)). A) Factors the denominator incorrectly. B) Gets the sign in the denominator factor wrong. D) Cancels terms instead of factors.

Rational Expressions and Functions flashcards

4 cards from the 11 in this chapter.

Domain of f(x) = 1/(x − 5)?

All real numbers except x = 5.

Worked Example: Solve the rational equation 1/(x − 1) + 2/x = 3/(x(x − 1)) and check for extraneous solutions.

Step 1: Identify restrictions (values that make any denominator zero). x ≠ 0, x ≠ 1 Step 2: Multiply every term by the LCD x(x − 1). x(x − 1)·[1/(x − 1)] + x(x − 1)·[2/x] = x(x − 1)·[3/(x(x − 1))] x + 2(x − 1) = 3 Step 3: Simplify and solve. x + 2x − 2 = 3 3x − 2 = 3 3x = 5 x = 5/3 Step 4: Check that x = 5/3 is not in the restriction set. 5/3 ≠ 0 and 5/3 ≠ 1 ✓ (not extraneous) Step 5: Verify by substitution. 1/(5/3 − 1) + 2/(5/3) = 1/(2/3) + 2·(3/5) = 3/2 + 6/5 = 15/10 + 12/10 = 27/10 3/((5/3)·(2/3)) = 3/(10/9) = 27/10 ✓ Final answer: x = 5/3.

What's an 'asymptote'?

A line the graph approaches as x or y grows without bound. A graph never crosses a vertical asymptote but can cross a horizontal one.

What is a 'rational expression'?

A fraction where numerator and denominator are polynomials.

Practise the full chapter

These are a sample. The full Rational Expressions and Functions chapter runs 27 items with per-chapter progress tracking, on the web and in the iOS app.

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