SAT Equivalent Expressions

Equivalent expressions questions ask you to rewrite an expression without changing its value — factoring, expanding, or simplifying a rational expression. Cancelling only part of a common factor is the error the bank returns to most.

Practise this skill freeHow the SAT is structured
MathAdvanced Math120 questions
The trap on this skill

Canceling only part of the common factor or keeping the factor that should cancel.

How this skill behaves

What 120 questions on it look like

88% of these questions can appear in the harder second module. On a section-adaptive test that matters: this is a skill that keeps mattering after a strong first module, not one you leave behind.

43% of the bank for this skill is rated hard, so it rewards practice past the point where the basic form feels comfortable.

medium46%
hard43%
easy12%

Difficulty mix across the 120 questions in this skill.

From the bank

Three real equivalent expressions questions

Each one explains the credited answer and why every other option fails.

Advanced Math · hard

For a rational expression connected with the greenway upper tripod printing shift log, x is restricted so that x != -1. Which expression is equivalent to (2x^2 - 6x - 8)/(2x + 2)?

  1. Ax + 1
  2. Bx - 4correct
  3. C2x - 4
  4. D(x - 4)/(x + 1)
Why B is correct — and why the others are not

Factor the numerator as 2(x + 1)(x - 4) and the denominator as 2(x + 1). Since x != -1, the common factor can be canceled, leaving x - 4. The key support is the way the item treats Equivalent expressions. A final check is separating the setup step from the final interpretation.

A. This value results from canceling only part of the common factor or keeping the factor that should cancel

C. This value results from canceling only part of the common factor or keeping the factor that should cancel

D. This value results from canceling only part of the common factor or keeping the factor that should cancel

Advanced Math · easy

In a simplification step for the workshop lower valve stacking usage chart, the expression (3x^2 - 9x - 30)/(3x + 6) is used with the condition x != -2. Which expression is equivalent to it?

  1. Ax + 2
  2. B3x - 5
  3. Cx - 5correct
  4. D(x - 5)/(x + 2)
Why C is correct — and why the others are not

Factor the numerator as 3(x + 2)(x - 5) and the denominator as 3(x + 2). Since x != -2, the common factor can be canceled, leaving x - 5. This is the only choice that stays consistent with the detail about Equivalent expressions. A final check is confirming that the selected expression has the same domain.

A. This value results from canceling only part of the common factor or keeping the factor that should cancel

B. This value results from canceling only part of the common factor or keeping the factor that should cancel

D. This value results from canceling only part of the common factor or keeping the factor that should cancel

Advanced Math · medium

For a rational expression connected with the lakeside east ramp timing ledger, x is restricted so that x != -5. Which expression is equivalent to (2x^2 - 6x - 80)/(2x + 10)?

  1. Ax + 5
  2. Bx - 8correct
  3. C2x - 8
  4. D(x - 8)/(x + 5)
Why B is correct — and why the others are not

Factor the numerator as 2(x + 5)(x - 8) and the denominator as 2(x + 5). Since x != -5, the common factor can be canceled, leaving x - 8. This matches the evidence or condition involving Equivalent expressions. A final check is checking whether a calculator result answers the actual question.

A. This value results from canceling only part of the common factor or keeping the factor that should cancel

C. This value results from canceling only part of the common factor or keeping the factor that should cancel

D. This value results from canceling only part of the common factor or keeping the factor that should cancel

120 questions on this skill, free to start.

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FAQ

Equivalent Expressions questions

When can I cancel in a fraction?

Only a factor of the entire numerator and the entire denominator. A term that is added, not multiplied, cannot be cancelled.

How do I check an equivalence quickly?

Substitute a convenient number into both expressions. If they disagree once, they are not equivalent.
Last reviewed 2026-08-28. Format and scoring facts sourced to College Board. Question counts describe the PrepScore bank, not the exam.
Same domain
Quadratic Functions and Equations135 questionsNonlinear Equations in One Variable127 questionsExponential Functions and Equations113 questionsPolynomial / Rational Expressions112 questions

Practise equivalent expressions until the trap stops working.

Real Digital SAT questions, the reasoning on every option, and a mistake bank that only clears when you get it right.

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