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Equivalent expressions — SAT practice questions

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Practice 146 Equivalent expressions questions in the app

What this topic is

Equivalent expressions look different but give the same value for every allowed input.

Questions ask which choice is equivalent to a given polynomial, rational expression, or expression with exponents and radicals. Useful tools include factoring, expanding products, combining fractions over a common denominator, and the rules of exponents.

A frequent error is expanding a squared sum as the sum of the squares; the square of x + a also includes a middle term, twice a times x. When the algebra stalls, substituting a simple number into the original and into each choice exposes the match.

Sample questions

Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.

Question 1Mid

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

\frac{3 x + 6}{x - 3}

✗ Not this one

\frac{3}{x - 3}

✗ Not this one

\frac{3 x + 6}{x^{2} - 9}

✓ Correct

\frac{2 x + 6}{x^{2} - 9}

✗ Not this one

Show answer

Answer: C — $\frac{3 x + 6}{x^{2} - 9}$

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

Question 2Easier

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

8 x

✗ Not this one

16 x

✓ Correct

2 x^{2} + 32

✗ Not this one

x^{2} - 16

✗ Not this one

Show answer

Answer: B — $16 x$

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

Question 3Easier

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

x

✗ Not this one

x^{5 / 9}

✗ Not this one

x^{4 / 3}

✗ Not this one

x^{2}

✓ Correct

Show answer

Answer: D — $x^{2}$

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

Every question is picked for where you are right now, wrong answers come back until they stick, and it all works offline.

Practice 146 Equivalent expressions questions in the app

Equivalent expressions — SAT practice questions

What this topic is

Sample questions

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