SAT Math · Equivalent expressions · medium
For which values of x is the expression (x²-4)/(x²-2x) undefined?
For which values of is the expression undefined?
Answer and explanation
Answer: D: x=0 and x=2
An expression is undefined where its denominator equals zero. Factor the denominator: , which is zero when or . That makes the answer D. Although the numerator shares the factor with the denominator, canceling would hide the problem at , but the original expression is still undefined there. Choice A misses . Choice B uses the zeros of the numerator, , which are where the expression equals zero (or is a hole) and not where it is undefined. Choice C misses .
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