+367 Question 1.
There are numbers a and b for which
Ax−1+Bx+1=x+2x2−1
for every number x≠±1. Find b.
Question 2.
If h>0, find all values of h such that ⌈h⌉⋅⌊h⌋=72. Express your answer using interval notation.
+130466 (1) Note x^2 - 1 = (x - 1) (x + 1)
x + 2 A B
____________ = _______ + _____ multiply through by (x - 1) ( x + 1)
(x - 1) ( x + 1) x - 1 x + 1
x + 2 = A ( x + 1) + B ( x - 1) simplify as
1x + 2 = (A + B)x + (A - B)
Equating terms we have that
A + B = 1
A - B = 2 add these equations
2A = 3
A = 3/2
And
3/2 + B = 1
B = -1/2
CORRECTED ANSWER !!!
