Write the Partial Fraction Decomposition of the Rational Expression $\frac { 5 } { x ^ { 2 } + 5 x }$

question 157

Multiple Choice

Write the partial fraction decomposition of the rational expression.Check your result algebraically. $\frac { 5 } { x ^ { 2 } + 5 x }$

• A) \(\frac { A } { x } + \frac { B } { x - 5 }\)
• B) \(\frac { 1 } { x } - \frac { 1 } { x + 5 }\)
• C) \(\frac { 1 } { x } + \frac { 1 } { x + 5 }\)
• D) \(\frac { A } { x } - \frac { B } { x - 5 }\)
• E) \(\frac { 1 } { x } - \frac { 1 } { x - 5 }\)

---

Definitions:

Central-plan Form

An architectural layout designed with a primary central space surrounded by symmetrical areas on each side, common in many churches and public buildings.

Hemispherical Dome

A type of dome that forms half of a perfect sphere, often used in architecture to cover large circular spaces.

Emperor Leo III

Byzantine Emperor known for initiating the policy of iconoclasm, which involved the destruction of religious images, leading to extensive controversy and conflict within the Empire.

Iconoclasm

The destruction of religious or sacred images. In Byzantium, the period from 726 to 843 when there was an imperial ban on such images. The destroyers of images were known as iconoclasts. Those who opposed such a ban were known as iconophiles.