Partial Fractions: 1/(x(x + 1)(x + 2))
1/(x(x + 1)(x + 2)) decomposes into (1/2)/x + -1/(x + 1) + (1/2)/(x + 2). A worked three linear factors example with the factorisation, the coefficient system, and an editable calculator.
1/(x(x + 1)(x + 2)) = (1/2)/x + -1/(x + 1) + (1/2)/(x + 2). Three distinct roots, three constants — the Heaviside cover-up method is fastest here.
e.g. 3x+11
Expanded or factored, e.g. (x-2)(x+3) or x^2+x-6
The decomposition
1/(x(x + 1)(x + 2)) = (1/2)/x + -1/(x + 1) + (1/2)/(x + 2)
Denominator factors: x × (x + 1) × (x + 2)
This is a three linear factors problem. Three distinct roots, three constants — the Heaviside cover-up method is fastest here.
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Frequently asked questions
How does 1/(x(x + 1)(x + 2)) decompose? ▾
1/(x(x + 1)(x + 2)) = (1/2)/x + -1/(x + 1) + (1/2)/(x + 2). Three distinct roots, three constants — the Heaviside cover-up method is fastest here.
How was the denominator factored? ▾
It factors as x × (x + 1) × (x + 2), which sets the shape of the decomposition.
How do I check the answer? ▾
Add the resulting fractions back over a common denominator — you should recover the original expression. Substituting a convenient value of x into both sides is a quicker spot check.
About this Calculator
1/(x(x + 1)(x + 2)) decomposes into (1/2)/x + -1/(x + 1) + (1/2)/(x + 2). A worked three linear factors example with the factorisation, the coefficient system, and an editable calculator.