+0

# Algebra

0
99
1

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
+9461
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