Question

Write out the form of the partial fraction decomposition of the function (as in this example). Do not determine the numerical values of the coefficients. ) x2 x2 x 6

Answer 1

The answer is "
`(A)/((x-2)) + (B)/((x+3))`"

Explanation:

Let the given value is:
`(x-6)/(x^2+x-6)`

`\to (x-6)/(x^2+x-6)=(x-6)/(x^2+(3-2)x-6)\\\\`

`=(x-6)/(x^2+(3-2)x-6)\\\\ =(x-6)/(x^2+3x-2x-6)\\\\ =(x-6)/(x(x+3)-2(x+3))\\\\ =(x-6)/((x+3)(x-2))\\\\=(A)/((x-2)) + (B)/((x+3))`