The partial fraction decomposition of latex: {x-9}/{x^2-3x-18} is latex: {a}/{x-6}+{b}/{x+3}. find the numbers latex: a and latex: b . then, find the sum latex: a + b, which is a whole number? enter that whole number as your answer.

The numbers are and , and the sum of is 1.

Step-by-step explanation:

We already know that the partial fraction decomposition of the rational fraction has a particular form, that is

.

So, the method to find the coefficients and is:

First: We calculate the sum .

So,

.

Notice that

,

which means that necessarily

.

Second: We equalize the coefficients of the same powers of .

The last equality we have obtained means that

and .

From the above statement we deduce that .

Third: We obtain a linear system of equations, with the unknowns and .

The solutions to these system of equations are   and

mxb67

step-by-step explanation:

throw the computer

step-by-step explanation: