Find the missing numerator and denominator.
-$$\frac { ( x - 10 ) ( x - 8 ) } { ( x - 4 ) ( x - 7 ) } \cdot \frac { ? } { ? } = \frac { ( x - 8 ) ( x - 11 ) } { ( x - 4 ) ( x - 2 ) }$$
A) $\frac { ( x + 11 ) ( x - 7 ) } { ( x + 2 ) ( x - 10 ) }$

B) $\frac { ( x - 11 ) ( x + 7 ) } { ( x - 2 ) ( x + 10 ) }$

C) $\frac { ( x + 11 ) ( x + 7 ) } { ( x + 2 ) ( x + 10 ) }$

D) $\frac { ( x - 11 ) ( x - 7 ) } { ( x - 2 ) ( x - 10 ) }$

Question

Find the missing numerator and denominator.
-$$\frac { ( x - 10 ) ( x - 8 ) } { ( x - 4 ) ( x - 7 ) } \cdot \frac { ? } { ? } = \frac { ( x - 8 ) ( x - 11 ) } { ( x - 4 ) ( x - 2 ) }$$
A) $\frac { ( x + 11 ) ( x - 7 ) } { ( x + 2 ) ( x - 10 ) }$

B) $\frac { ( x - 11 ) ( x + 7 ) } { ( x - 2 ) ( x + 10 ) }$

C) $\frac { ( x + 11 ) ( x + 7 ) } { ( x + 2 ) ( x + 10 ) }$

D) $\frac { ( x - 11 ) ( x - 7 ) } { ( x - 2 ) ( x - 10 ) }$

Quizplus · Accepted Answer

To find the missing fraction, we can set up the equation as follows: $$\frac { ( x - 10 ) ( x - 8 ) } { ( x - 4 ) ( x - 7 ) } \cdot \frac { ? } { ? } = \frac { ( x - 8 ) ( x - 11 ) } { ( x - 4 ) ( x - 2 ) }$$To solve for the missing fraction, we divide both sides by $\frac { ( x - 10 ) ( x - 8 ) } { ( x - 4 ) ( x - 7 ) }$, which simplifies to: $$\frac { ? } { ? } = \frac { ( x - 8 ) ( x - 11 ) } { ( x - 4 ) ( x - 2 ) } \div \frac { ( x - 10 ) ( x - 8 ) } { ( x - 4 ) ( x - 7 ) }$$This simplifies further to: $$\frac { ? } { ? } = \frac { ( x - 11 ) ( x - 7 ) } { ( x - 2 ) ( x - 10 ) }$$Therefore, the missing fraction is $\frac { ( x - 11 ) ( x - 7 ) } { ( x - 2 ) ( x - 10 ) }$, which matches option D.