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

Answer:

The answer is "$\frac{A}{(x-2)} + \frac{B}{(x+3)}$"

Step-by-step explanation:

Let the given value is: $\frac{x-6}{x^2+x-6}$

$\to \frac{x-6}{x^2+x-6}=\frac{x-6}{x^2+(3-2)x-6}$

                $=\frac{x-6}{x^2+(3-2)x-6}\\\\ =\frac{x-6}{x^2+3x-2x-6}\\\\ =\frac{x-6}{x(x+3)-2(x+3)}\\\\ =\frac{x-6}{(x+3)(x-2)}\\\\=\frac{A}{(x-2)} + \frac{B}{(x+3)}$