Final answer:
To perform a partial fraction decomposition, we need to break the given function into simpler fractions. In this case, we have a function with a quadratic denominator, so we need to decompose it into two fractions with linear denominators. We can represent the partial fraction decomposition as 1/(x-1)(x+2) = A/(x-1) + B/(x+2), where A and B are coefficients.
Step-by-step explanation:
The given function can be written as:
1/((x-1)(x+2))
To perform a partial fraction decomposition, we need to decompose this expression into simpler fractions. In this case, we have a quadratic denominator, so we can break it down into two simpler fractions with linear denominators:
1/(x-1)(x+2) = A/(x-1) + B/(x+2)
Where A and B are coefficients to be determined.
By finding a common denominator and combining like terms, we can solve for A and B using the original expression. However, we are only asked to write the form of the partial fraction decomposition, not the numerical values of the coefficients.