Find the missing numerator and denominator.
-$$\frac { 7 x ^ { 2 } - 28 x } { x ^ { 2 } - 6 x - 40 } \div \frac { ? } { ? } = \frac { 7 x } { x - 10 }$$
A) $\frac { x - 10 } { 7 x }$

B) $\frac { x + 10 } { 7 x }$

C) $\frac { x - 4 } { x + 4 }$

D) $\frac { 7 x } { x + 10 }$

Question

Find the missing numerator and denominator.
-$$\frac { 7 x ^ { 2 } - 28 x } { x ^ { 2 } - 6 x - 40 } \div \frac { ? } { ? } = \frac { 7 x } { x - 10 }$$
A) $\frac { x - 10 } { 7 x }$

B) $\frac { x + 10 } { 7 x }$

C) $\frac { x - 4 } { x + 4 }$

D) $\frac { 7 x } { x + 10 }$

Quizplus · Accepted Answer

To divide by a fraction, we invert and multiply. Thus, we need to find the reciprocal of the fraction on the right-hand side of the equation: $\frac{x-10}{7x}$. This is $\frac{7x}{x-10}$. Therefore, we have $$\frac { 7 x ^ { 2 } - 28 x } { x ^ { 2 } - 6 x - 40 } \cdot \frac { x-10 } { 7 x } = \frac { 7 x } { x - 10 }.$$ Simplifying the left-hand side, we have $$\frac{7x(x-4)}{(x-10)(x+4)} \cdot \frac{x-10}{7x} = \frac{7x}{x-10}.$$ The $7x$ factors cancel, leaving $\frac{x-4}{x+4}$ as the missing fraction. Therefore, the answer is $\boxed{\text{(C)}}$.

Find the Missing Numerator and Denominator 7x2−28xx2−6x−40÷??=7xx−10\frac { 7 x ^ { 2 } - 28 x } { x ^ { 2 } - 6 x - 40 } \div \frac { ? } { ? } = \frac { 7 x } { x - 10 }x2−6x−407x2−28x​÷??​=x−107x​

Find the Missing Numerator and Denominator $\frac { 7 x ^ { 2 } - 28 x } { x ^ { 2 } - 6 x - 40 } \div \frac { ? } { ? } = \frac { 7 x } { x - 10 }$