Question #5bed0

1 Answer
Jan 1, 2018

The answer is #=1/(x-2)-1/(x-1)^2-1/(x-1)#

Explanation:

Perform the decomposition into partial fractions

#1/((x-2)(x-1)^2)=A/(x-2)+B/(x-1)^2+C/(x-1)#

#=(A(x-1)^2+B(x-2)+C(x-2)(x-1))/((x-2)(x-1)^2)#

The denominators are the same, compare the numerators

#1=A(x-1)^2+B(x-2)+C(x-2)(x-1)#

Let #x=2#, #=>#, #A=1#

Let #x=1#, #=>#, #B=-1#

Coefficients of #x^2#

#0=A+C#, #=>#, #C=-1#

Therefore,

#1/((x-2)(x-1)^2)=1/(x-2)-1/(x-1)^2-1/(x-1)#