Since the denominator of the fraction is a repeated linear factor `(ax+b)^n` , its partial fraction decomposition is in the form:
To determine the values of of A1 and A2, simplify the equation by multiplying both sides by the LCD of the three fractions.
`2x+1=A_1(x-1)+A_2` (Let this be EQ1.)
Then, assign a value to x, such that A1 will be eliminated. And only A2 remains in the equation.
To do so, let x=1.
Now that value of A2 is known, plug-in this to EQ1.
Then, assign another value to x.
Let it be x=0.
Hence, ` (2x+1)/(x-1)^2=2/(x-1)+3/(x-1)^2` .
(For the second problem, kindly post it as a separate question in Homework Help.)