+789 Find constants A and B such that
(x + 17)/(x^2 - x - 2) = A/(x - 2) + B/(x + 1)
for all x such that $x \neq -1$ and $x \neq 2$. Give your answer as the ordered pair (A,B).
+410 This is pretty simple partial fraction decomposition.
Our first indication that partial fraction decomposition works is (x−2)(x+1)=x2−x−2
x+17x2−x−2=Ax−2+Bx+1, and we make the denominators equal, x+17x2−x−2=A(x+1)(x+1)(x−2)+B(x−2)(x+1)(x−2), and x+17=A(x+1)+B(x−2). To solve, we plug in some special values, like 2, so 19 = 3A, A = 19/3. Similarly, by plugging in -1, we get B = -16/3. So out answer is A = 19/3, B = -16/3.
+410 This is pretty simple partial fraction decomposition.
Our first indication that partial fraction decomposition works is (x−2)(x+1)=x2−x−2
x+17x2−x−2=Ax−2+Bx+1, and we make the denominators equal, x+17x2−x−2=A(x+1)(x+1)(x−2)+B(x−2)(x+1)(x−2), and x+17=A(x+1)+B(x−2). To solve, we plug in some special values, like 2, so 19 = 3A, A = 19/3. Similarly, by plugging in -1, we get B = -16/3. So out answer is A = 19/3, B = -16/3.
