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

question 68

Multiple Choice

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. $\frac { 9 } { a - 7 } - \frac { 5 } { 7 - a }$

• A) \(- \frac { 15 } { 7 - a }\)
• B) \(\frac { 14 } { a - 7 }\)
• C) \(\frac { 9 } { 7 - a }\)
• D) \(\frac { 14 } { 7 - a }\)

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Definitions:

Antecedent

The “if” component in a hypothetical proposition.

Hypothetical Proposition

An assumption or proposition made for the sake of argument that explores consequences of its being true, regardless of its actual truth value.

Antecedent

In logic and grammar, it refers to the conditional clause or phrase to which a pronoun refers back; in logic, also the first part of a conditional statement.

Consequent

The “then” component in a hypothetical proposition.