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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