Multiply.
-$\frac { x - 8 } { x - 1 } \cdot \frac { 1 - x } { 8 - x }$
A)- 8
B)8
C)-1
D)1

Question

Quizplus · Accepted Answer

The numerator and denominator of the first fraction can be rewritten as:$$\frac { x - 8 } { x - 1 } = \frac { ( x - 1 ) - 7 } { x - 1 } = 1 - \frac { 7 } { x - 1 }$$The numerator and denominator of the second fraction can be rewritten as:$$\frac { 1 - x } { 8 - x } = \frac { - ( x - 1 ) } { - ( x - 8 ) } = - \frac { x - 1 } { x - 8 }$$So, the product of the two fractions is:$$\left( 1 - \frac { 7 } { x - 1 } \right) \left( - \frac { x - 1 } { x - 8 } \right) = - \left( 1 - \frac { 7 } { x - 1 } \right) = -1 + \frac { 7 } { x - 1 }$$This is equal to choice D.

Multiply - x−8x−1⋅1−x8−x\frac { x - 8 } { x - 1 } \cdot \frac { 1 - x } { 8 - x }x−1x−8​⋅8−x1−x​

Multiply
- $\frac { x - 8 } { x - 1 } \cdot \frac { 1 - x } { 8 - x }$