+0

# rational expressions of polynomials

-1
90
1
+204

Find the product CD of the integers C and D for which

$\frac{C}{x-3}+\frac{D}{x+8}=\frac{4x-23}{x^2+5x-24}$
for all real values of x except -8 and 3.

Feb 25, 2021

#1
+8457
+1

Multiply through by $$x^2 + 5x - 24$$.

For all real values of x except -8 and 3,

$$C(x + 8) + D(x - 3) = 4x - 23\\ (C + D)x + (8C - 3D) = 4x - 23$$

Comparing coefficients,

$$\begin{cases}C + D = 4\\8C - 3D = -23\end{cases}$$

Solving, (C, D) = (-1, 5).

Therefore CD = -5.

Feb 25, 2021