+0  
 
0
39
1
avatar

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.

 Jun 1, 2022
 #1
avatar+9457 
0

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?

 Jun 2, 2022

7 Online Users

avatar
avatar