Step 1

By long division, divide the denominator into the numerator. The result is

Step 2 (1)

Break up the remainder into a sum,

One can readily check that Equation 1 is true,

The terms and are called partial fractions. Later on we shall

explain how they were found. Notice that the denominators of the partial fractions are factors of the denominator of the rational function,

(x + 2)(x - 5) = x² - 3x - 10.

Step 3

We now have