Divide and simplify.
-$$\frac { x ^ { 2 } + 6 x + 9 } { x ^ { 2 } + 10 x + 21 } \div \frac { x ^ { 2 } + 3 x } { x ^ { 2 } + 12 x + 35 }$$
A) $\frac { x + 5 } { x }$
B) $x + 5$
C) $\frac { x } { x ^ { 2 } + 10 x + 21 }$
D) $\frac { x + 5 } { x ^ { 2 } + 7 x }$

Question

Quizplus · Accepted Answer

First, factorize all polynomials: $\frac{(x+3)^2}{(x+7)(x+3)} \div \frac{x(x+3)}{(x+7)(x+5)}$. Simplify by flipping the second fraction and multiplying: $\frac{(x+3)^2}{(x+7)(x+3)} \cdot \frac{(x+7)(x+5)}{x(x+3)}$. Cancel common factors to get $\frac{x+5}{x}$.

Divide and Simplify x2+6x+9x2+10x+21÷x2+3xx2+12x+35\frac { x ^ { 2 } + 6 x + 9 } { x ^ { 2 } + 10 x + 21 } \div \frac { x ^ { 2 } + 3 x } { x ^ { 2 } + 12 x + 35 }x2+10x+21x2+6x+9​÷x2+12x+35x2+3x​

Divide and Simplify $\frac { x ^ { 2 } + 6 x + 9 } { x ^ { 2 } + 10 x + 21 } \div \frac { x ^ { 2 } + 3 x } { x ^ { 2 } + 12 x + 35 }$