Perform the indicated operations. Simplify if possible.
-$$\left( \frac { 3 x ^ { 2 } - 4 x - 4 } { x ^ { 2 } + 2 x - 3 } \cdot \frac { x ^ { 2 } + 3 x - 4 } { 12 x ^ { 2 } + 11 x + 2 } \right) \div \frac { 3 x ^ { 2 } - 5 x - 2 } { 8 x ^ { 2 } - 2 x - 1 }$$
A) 1
B) $\frac { ( x + 4 ) } { ( x + 3 ) }$
C) $\frac { 3 x + 1 } { 2 x - 1 }$
D) $\frac { ( x + 4 ) ( 2 x - 1 ) } { ( x + 3 ) ( 3 x + 1 ) }$

Question

Quizplus · Accepted Answer

To solve this, first factorize each polynomial where possible, then simplify by canceling out common factors. The division by a fraction is equivalent to multiplying by its reciprocal. After simplification, the result matches option D.

Perform the Indicated Operations A) 1 B) (x+4)(x+3)\frac { ( x + 4 ) } { ( x + 3 ) }(x+3)(x+4)​

Perform the Indicated Operations A) 1
B) $\frac { ( x + 4 ) } { ( x + 3 ) }$