How do you express 1/((x+7)(x^2+9))1(x+7)(x2+9) in partial fractions?
1 Answer
Apr 15, 2016
Explanation:
Working with Real coefficients, the factor
So we want to find a decomposition of the form:
1/((x+7)(x^2+9)) = A/(x+7) + (Bx+C)/(x^2+9)
=(A(x^2+9)+(Bx+C)(x+7))/((x+7)(x^2+9))
=((A+B)x^2+(7B+C)x+(9A+7C))/((x+7)(x^2+9))
Equating coefficients, we get the following system of simultaneous linear equations:
{(A+B=0),(7B+C=0),(9A+7C=1):}
Hence:
{(A=1/58),(B=-1/58),(C=7/58):}
So:
1/((x+7)(x^2+9)) = 1/(58(x+7)) + (7-x)/(58(x^2+9))