Please provide a neat complete and accurate solution to part

Please provide a neat, complete, and accurate solution to part a, and b neatly using Ms equation editor showing all steps!!!

Thank you,

(1) Write the partial fraction decomposition of the rational expres- sion. a is a constant. 2

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

= A/(a+x) +B/(a-x)

= A(a-x) +B(a+x)

1= aA +aB +x( -A +B)

Equating the coefficients:

aA + aB = 1

and -A +B =0 ----> A = B

So, aA +aA =1 ----> A = 1/2a

B = 1/2a

So, 1/(a^2 -x^2) = 1/2a(a+x) +1/2a(a -x)

b) 1/x(x+a) = A/x +B/(x+a)

1 = A(x+a) + Bx

1= x(A+B) + aA

Onequating the coefficients:

aA =1 ----> A = 1/a

A+B =0 ----> B = -1/a

So,

1/x(x+a) = 1/a*x - 1/a(x+a)