Given:
Rational expression is
[tex]\frac{20}{x(x-5)}[/tex]
Required:
Write the partial fraction decomposition of the given rational expression.
Explanation:
We will solve rational expression as:
[tex]\begin{gathered} \frac{20}{x(x-5)}=\frac{A}{x}+\frac{B}{x-5} \\ \frac{20}{x(x-5)}=\frac{A(x-5)+Bx}{x(x-5)} \\ (A+B)x-5A=20 \end{gathered}[/tex]
Now, we will compare LHS and RHS
A+B=0
-5A=20
A= - 4 and B=4
Now,
[tex]\frac{20}{x(x-5)}=\frac{-4}{x}+\frac{4}{x-5}[/tex]
Answer:
Hence, above is the answer.
