Advanced MathVery hardConstants in a combined fraction
Advanced Math practice question
For x > 0, the sum 1/x + 1/(x + 1) can be written as (ax + b)/(x(x + 1)), where a and b are constants. What is the value of a + b?
Answer: 3
Common denominator x(x + 1): (x + 1)/(x(x + 1)) + x/(x(x + 1)) = (2x + 1)/(x(x + 1)). So a = 2, b = 1, and a + b = 3.
Common wrong answers
- If you answered 1
- 1 is b alone.
- If you answered 2
- 2 is a alone (or a + b if the +1 from the first numerator is dropped).
- If you answered 4
- 4 would come from a numerator of 2x + 2, adding (x + 1) twice.
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