SAT · Passport to Advanced Math · Rational expressions and equations
Question sat-q-00093
Medium Multiple choice No calculator
The question
For what value of x is the expression (x + 7) / (x − 8) undefined?
- -7
- 8
- 7
- -8
Show answer & worked solution
Answer: 8
Worked solution. A rational expression is undefined when its denominator equals zero. Set x − 8 = 0, so x = 8.
Why each wrong choice is wrong. Sign-flip distractors are everywhere here. Students who see (x − 8) and answer −8 are extracting the wrong root.
Test-day tactic. Restricted values come from setting the denominator equal to zero, then solving — the numerator is irrelevant.
About this question type
A rational expression is a ratio of two polynomials. SAT items ask you to simplify, to identify restricted values where the denominator equals zero, to add or subtract two rational expressions, or to solve a rational equation by clearing denominators.
You will see a question shaped like this one on roughly every other official SAT form, typically at a moderate position in the section — solidly within the range that separates a 600-band student from a 700-band student. Treat any miss in this subtopic as a signal to drill the subtopic page before you do another full practice test.