\(\rm\frac{X}{(X+2)(X−3)}\) =

Let's solve it using partial diffraction:

\(\rm\frac{X}{(X+2)(X−3)}= \rm\frac{A}{(X+2)}+\rm\frac{B}{(X−3)} ~~~~~---- Eq(i) \\ \therefore \rm\frac{X}{(X+2)(X−3)}= \rm\frac{A(x-3)+B(x+2)}{(x +2)(X-3)} \\ \Rightarrow \rm\frac{X}{(X+2)(X−3)}= \rm\frac{x(A+B)+2B-3A}{(x +2)(X-3)} \)

Now comparing both sides:

A + B = 1  ----- ---Eq(ii)

-3A + 2B = 0  ----Eq(iiI)

after solving the above equations, we get:

\(\rm{A = \frac{2}{5}\ \& ~ B = \frac{3}{5}} \)

after putting these value in Eq(i), we will get:

\(\rm\frac{X}{(X+2)(X−3)} = \rm\frac{2}{5(X+2)}+\frac{3}{5(X−3)}\)