Advanced MathVery hardSimplifying with a difference of squares
Advanced Math practice question
If a ≠ b and (a² − b²)/(a − b) = 11, what is the value of a + b?
Answer: 11
a² − b² = (a − b)(a + b). Dividing by (a − b) cancels it (allowed since a ≠ b), leaving a + b = 11.
Common wrong answers
- If you answered 0
- 0 would mean a = −b, but then a² − b² = 0 and the fraction would be 0, not 11.
- If you answered 121
- 121 is 11², squaring the result. The expression simplifies directly to a + b.
- If you answered 5.5
- 5.5 halves 11; nothing in the simplification divides by 2.
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