For x ≠ 0, −1, −2 the sum 1/(x(x + 1)) + 1/((x + 1)(x + 2)) equals:

Question

Accepted Answer

2/(x(x + 2)). Split each term: 1/(x(x + 1)) = 1/x − 1/(x + 1) and 1/((x + 1)(x + 2)) = 1/(x + 1) − 1/(x + 2). Adding, the middle terms cancel, leaving 1/x − 1/(x + 2) = 2/(x(x + 2)). (At x = 1: 1/2 + 1/6 = 2/3.)

For $x$ ≠ 0, −1, −2 the sum $1/ (x (x + 1)) + 1/ ((x + 1) (x + 2))$ equals:

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More Algebra practice

For x ≠ 0, −1, −2 the sum 1/(x(x+1))+1/((x+1)(x+2)) equals:

Step-by-Step Solution

Master this topic in 30 minutes a day.

More Algebra practice

For $x$ ≠ 0, −1, −2 the sum $1/ (x (x + 1)) + 1/ ((x + 1) (x + 2))$ equals: