Resolve the expression into the simplest partial fractions

The partial fraction expansion will look like

(x - 2)/((x ² + 1) (x - 1)²) = (ax + b)/(x ² + 1) + c/(x - 1) + d/(x - 1)²

Get everything in terms of a common denominator, and compare the numerators on both sides:

x - 2 = (ax + b) (x - 1)² + c (x ² + 1) (x - 1) + d (x ² + 1)

Expand the right side:

x - 2 = (ax + b) (x - 1)² + c (x ² + 1) (x - 1) + d (x ² + 1)

x - 2 = (a + c) x ³ + (-2a + b - c + d) x ² + (a - 2b + c) x + b - c + d

Match up the coefficients and solve the resulting system of equations:

a + c = 0

-2a + b - c + d = 0

a - 2b + c = 1

b - c + d = -2

==>   a = -1, b = -1/2, c = 1, d = -1/2

So the expansion into partial fractions is

(x - 2)/((x ² + 1) (x - 1)²) = (-x - 1/2)/(x ² + 1) + 1/(x - 1) - 1/(2 (x - 1)²)

… = -(2x + 1)/(2 (x ² + 1)) + 1/(x - 1) - 1/(2 (x - 1)²)

correct choice is b

step-by-step explanation:

when you calculate the average rate of change of a function, you are finding the slope of the secant line between the two points. for the function the average rate of change from point to point can be calculated as

to find the average rate of change from day 2 to day 10, note that at day 2, 8 houses were sold, so a(2,8) and at day 10, 2 houses were sold, so b(10,2). thus,