Divide.
-$\frac { x + 4 } { x - 7 } \div \frac { x + 3 } { x - 5 }$

A) $\frac { ( x - 7 ) ( x + 3 ) } { ( x + 4 ) ( x - 5 ) }$

B) $\frac { ( x + 4 ) ( x + 3 ) } { ( x - 7 ) ( x - 5 ) }$

C) $\frac { ( x - 7 ) ( x - 5 ) } { ( x + 4 ) ( x + 3 ) }$

D) $\frac { ( x + 4 ) ( x - 5 ) } { ( x - 7 ) ( x + 3 ) }$

Question

Divide.
-$\frac { x + 4 } { x - 7 } \div \frac { x + 3 } { x - 5 }$

A) $\frac { ( x - 7 ) ( x + 3 ) } { ( x + 4 ) ( x - 5 ) }$

B) $\frac { ( x + 4 ) ( x + 3 ) } { ( x - 7 ) ( x - 5 ) }$

C) $\frac { ( x - 7 ) ( x - 5 ) } { ( x + 4 ) ( x + 3 ) }$

D) $\frac { ( x + 4 ) ( x - 5 ) } { ( x - 7 ) ( x + 3 ) }$

Quizplus · Accepted Answer

To divide fractions, we invert the second fraction and multiply, so we get:

$\frac { x + 4 } { x - 7 } \div \frac { x + 3 } { x - 5 } = \frac { x + 4 } { x - 7 } \cdot \frac { x - 5 } { x + 3 }$

Now we factor both the numerator and denominator and cancel any common factors:

$\frac { x + 4 } { x - 7 } \cdot \frac { x - 5 } { x + 3 } = \frac { ( x + 4 ) ( x - 5 ) } { ( x - 7 ) ( x + 3 ) }$

Therefore, the correct answer is D.

Divide - x+4x−7÷x+3x−5\frac { x + 4 } { x - 7 } \div \frac { x + 3 } { x - 5 }x−7x+4​÷x−5x+3​