Decompose P/Q, Where Q Has Repeated Linear Factors
Write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the
constants.
-$$\frac { 6 x - 5 } { ( x - 1 ) ( x - 6 ) ^ { 2 } }$$
A) $\frac { A } { x - 1 } + \frac { B } { x - 6 } + \frac { C } { ( x - 6 ) ^ { 2 } }$
B) $\frac { A } { x - 1 } + \frac { B } { x - 6 } + \frac { C } { x - 6 } + \frac { D x + E } { ( x - 6 ) ^ { 2 } }$
C) $\frac { \mathrm { A } } { \mathrm { x } - 1 } + \frac { \mathrm { B } } { \mathrm { x } - 6 } + \frac { \mathrm { Cx } + \mathrm { D } } { ( \mathrm { x } - 6 ) ^ { 2 } }$
D) $\frac { A } { x - 1 } + \frac { B } { x - 6 } + \frac { C } { x - 6 } + \frac { D } { ( x - 6 ) ^ { 2 } }$ Write the partial fraction decomposition of the rational expression.

Question

Quizplus · Accepted Answer

For a rational expression where the denominator has repeated linear factors, each factor $ (x - a)^n $ contributes terms $ \frac{A_1}{(x-a)} + \frac{A_2}{(x-a)^2} + \cdots + \frac{A_n}{(x-a)^n} $. Since $ (x - 6) $ is squared, it contributes $ \frac{B}{x - 6} + \frac{C}{(x - 6)^2} $, and $ (x - 1) $ contributes $ \frac{A}{x - 1} $.

Decompose P/Q, Where Q Has Repeated Linear Factors Write the Form

Decompose P/Q, Where Q Has Repeated Linear Factors
Write the Form