Find constants a and b such that (2x + 17)/(x^2 - x - 2) = a/(x - 2) + b/(x + 1) for all x such that x≠-1 and x≠2.
Since x≠-1 and x≠2, we can multiply both sides by \(x^2 - x - 2\).
\(2x + 17 = a\cdot (x + 1) + b\cdot (x - 2)\)
That means \((a + b)x + (a - 2b) = 2x + 17\). Then \(\begin{cases} a + b = 2\\ a - 2b = 17 \end{cases}\).
Can you take it from here?
