How do you write the partial fraction decomposition of the rational expression # (5x+7)/(x^2+4x-5)#?
The denominator may be factorized as a trinomial as follows :
Since these are 2 different linear factors, we may write the original expression in terms of partial fractions as follows :
Now comparing terms in the numerator yields the following set of linear equations which may be solved simultaneously :
Solving we get :
Hence the partial fraction decomposition is