Question

Hello, I need some assistance with this precalculus question, please?HW Q14

Answer 1

Given:

Rational expression is

`(20)/(x(x-5))`

Required:

Write the partial fraction decomposition of the given rational expression.

Step-by-step explanation:

We will solve rational expression as:

`\begin{gathered} (20)/(x(x-5))=(A)/(x)+(B)/(x-5) \\ (20)/(x(x-5))=(A(x-5)+Bx)/(x(x-5)) \\ (A+B)x-5A=20 \end{gathered}`

Now, we will compare LHS and RHS

A+B=0

-5A=20

A= - 4 and B=4

Now,

`(20)/(x(x-5))=(-4)/(x)+(4)/(x-5)`

Answer:

Hence, above is the answer.