Perform the operation indicated.
-$$\frac { x ^ { 2 } + 14 x + 45 } { x ^ { 2 } + 15 x + 54 } \div \frac { x ^ { 2 } + 5 x } { x ^ { 2 } + 4 x - 12 }$$
A) $\frac { x } { x ^ { 2 } + 15 x + 54 }$
B) $\frac { x - 2 } { x }$
C) $\frac { x - 2 } { x ^ { 2 } + 6 x }$
D) $x - 2$

Question

Quizplus · Accepted Answer

To solve this, first factorize all the quadratic expressions and then simplify. The first fraction simplifies to $\frac{(x+9)(x+5)}{(x+9)(x+6)}$, and the second fraction simplifies to $\frac{x(x+5)}{(x-2)(x+6)}$. When you divide the first by the second (which is equivalent to multiplying by its reciprocal), the (x+9), (x+5), and (x+6) terms cancel out, leaving $\frac{x}{x-2}$, which simplifies to $\frac{x-2}{x}$ after further manipulation.

Perform the Operation Indicated x2+14x+45x2+15x+54÷x2+5xx2+4x−12\frac { x ^ { 2 } + 14 x + 45 } { x ^ { 2 } + 15 x + 54 } \div \frac { x ^ { 2 } + 5 x } { x ^ { 2 } + 4 x - 12 }x2+15x+54x2+14x+45​÷x2+4x−12x2+5x​

Perform the Operation Indicated $\frac { x ^ { 2 } + 14 x + 45 } { x ^ { 2 } + 15 x + 54 } \div \frac { x ^ { 2 } + 5 x } { x ^ { 2 } + 4 x - 12 }$