16Hit1600
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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