Consider the Addition Problem $$\frac { 8 } { x - 2 } + \frac { 5 } { 2 - x }$$

question 240

Short Answer

Consider the addition problem. $$\frac { 8 } { x - 2 } + \frac { 5 } { 2 - x }$$ Note that the denominators are opposites of each other. If the property $$\frac { a } { - b } = - \frac { a } { b }$$ is applied to the second fraction, we have $$\frac { 5 } { 2 - x } = - \frac { 5 } { x - 2 }$$ Thus we proceed as follows: $$\frac { 8 } { x - 2 } + \frac { 5 } { 2 - x } = \frac { 8 } { x - 2 } - \frac { 5 } { x - 2 } = \frac { 8 - 5 } { x - 2 } = \frac { 3 } { x - 2 }$$ Use this approach to do the following problem. $$\frac { 9 } { a - 2 } - \frac { 1 } { 2 - a }$$

---

Definitions:

Reaction Mechanism

The step-by-step sequence of elementary reactions by which an overall chemical change occurs, detailing the molecular level changes.

Carboxylic Acid

Organic molecules that feature a carboxyl group (-COOH) are known for their acidic characteristics and are commonly found throughout the natural world.

Aldehyde

Organic compounds characterized by a carbon atom bonded to a hydrogen atom and double-bonded to an oxygen atom at the end of a carbon chain.

DIBAL

Diisobutylaluminum hydride, a reducing agent commonly used in organic synthesis to reduce esters, aldehydes, and ketones to alcohols.