The partial fraction of [tex]\frac{x+4}{x^{2} +x}[/tex] is as follows
[tex]\frac{x+4}{x^{2} +x} =-\frac{3}{x+1}+\frac{4}{x}[/tex]
Partial fraction is the result of writing a rational expression as the sum of two or more fractions.
Therefore,
[tex]\frac{x+4}{x^{2} +x} =\frac{A}{x+1}+\frac{B}{x}[/tex]
Let's find the zeros of (x + 1) and (x)
when x = -1
Ax + B(x + 1) = x + 4
x + 4 = A(-1) + B(-1 + 1)
-A = -1 + 4
A = -3
when x = 0
A(0) + B(0 + 1) = 0 + 4
B = 4
Therefore,
[tex]\frac{x+4}{x^{2} +x} =-\frac{3}{x+1}+\frac{4}{x}[/tex]
learn more on partial fraction here: https://brainly.com/question/24594390
