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

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. $$\frac { 9 } { a - 2 } - \frac { 1 } { 2 - a }$$