Short answer
What should you know first?
If algebra keeps slowing down your GRE Mathematics Subject Test prep, start with expression fluency: legal cancellation, factoring, exponents, radicals, and domain restrictions. This is the algebra layer that quietly blocks functions, calculus, and linear algebra when it stays shaky.
What to study here
Focus on the moves that actually change later work.
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Simplify multi-step expressions without introducing sign or domain errors.
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Rewrite expressions into equivalent forms that are easier to use later.
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Spot illegal cancellation and hidden restrictions instantly.
Why it matters
Why this topic changes the rest of your prep.
A student cannot move quickly on the GRE if every problem turns into a fight with fractions, exponents, radicals, or signs. The goal here is compression: enough fluency that working memory stays free for reasoning.
Must know
Facts and heuristics that should start feeling automatic.
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Only factors cancel. Terms across addition or subtraction do not.
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Negative exponents move factors across the fraction bar; they do not negate the whole expression.
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Excluded values come from the original denominator.
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Even roots over the reals require nonnegative radicands.
Useful cue
Re-express before you compute. • Check domain restrictions early.
Worked example
One representative example.
Simplify $$\frac{x^2-9}{x^2-3x}$$ and state all excluded values.
Long route
Factor numerator and denominator to get $$\frac{(x-3)(x+3)}{x(x-3)}$$. The original denominator excludes $$x=0$$ and $$x=3$$. Then cancel the common factor $$x-3$$ to get $$\frac{x+3}{x}$$ with the same exclusions.
Fast route
Factor immediately, cancel $$x-3$$, and keep the original restrictions $$x\ne 0,3$$.
Common traps
What usually breaks first.
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Canceling across addition.
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Forgetting excluded values after simplification.
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Mixing up negative exponents with negative numbers.
Quick questions
Short answers that searchers usually need first.
What should I study before algebra review for the GRE Mathematics Subject Test?
You can start here directly, then use the next linked pages to keep building outward from this topic.
Why does algebra review matter on the GRE Mathematics Subject Test?
A student cannot move quickly on the GRE if every problem turns into a fight with fractions, exponents, radicals, or signs. The goal here is compression: enough fluency that working memory stays free for reasoning.
What does algebra review unlock after it gets stronger?
Algebra review unlocks Factoring and polynomial algebra, Equations, inequalities, and absolute value, Matrices and linear systems inside the same dependency-first study graph.