Equivalent expressions — SAT practice questions

Equivalent expressions on the SAT Math test means rewriting an algebraic form so it matches another form that looks different but is identical for all allowed values of the variable. Students must factor, expand, combine like terms, and add or subtract rational expressions while honoring domain restrictions. Items usually ask which expression is equivalent to a given polynomial or fraction sum and present fully simplified, factored, or combined answer choices. Typical traps are sign errors when expanding squares, illegal cancellation of terms that are not factors, and rewrites that look close but fail under a stated restriction on x.

Section: Math 44 questions on the paper
140 practice questions in the app

Sample questions

Question 1

Which expression is equivalent to $\dfrac{2}{x-3}+\dfrac{x}{x^2-9}$ , where $x\ne3$ and $x\ne-3$ ?

A $\dfrac{3x+6}{x-3}$
B $\dfrac{3}{x-3}$
C $\dfrac{3x+6}{x^2-9}$
D $\dfrac{2x+6}{x^2-9}$

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Answer: C — $\dfrac{3x+6}{x^2-9}$

Note $x^2-9=(x-3)(x+3)$ . Rewrite the first fraction: $\dfrac{2(x+3)}{(x-3)(x+3)}+\dfrac{x}{(x-3)(x+3)}=\dfrac{2x+6+x}{(x-3)(x+3)}=\dfrac{3x+6}{x^2-9}$ .

Question 2

Which expression is equivalent to $(x+4)^2-(x-4)^2$ ?

A $8x$
B $16x$
C $2x^2+32$
D $x^2-16$

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Answer: B — $16x$

Using the difference of squares gives $[(x+4)-(x-4)][(x+4)+(x-4)]=8(2x)=16x$ .

Question 3

For $x>0$ , which expression is equivalent to $\sqrt[3]{x^5}\cdot x^{1/3}$ ?

A $x$
B $x^{5/9}$
C $x^{4/3}$
D $x^2$

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Answer: D — $x^2$

Adding exponents gives $x^{5/3}x^{1/3}=x^{6/3}=x^2$ .

Practice 140 Equivalent expressions questions in the app

Equivalent expressions — SAT practice questions

Sample questions

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Math