Divide.
-$$\frac { x ^ { 2 } + 11 x + 18 } { x ^ { 2 } + 15 x + 54 } \div \frac { x ^ { 2 } + 2 x } { x ^ { 2 } + 14 x + 48 }$$
A) $\frac { x + 8 } { x ^ { 2 } + 6 x }$

B) $\frac { x } { x ^ { 2 } + 15 x + 54 }$

C) $x + 8$

D) $\frac { x + 8 } { x }$

Question

Divide.
-$$\frac { x ^ { 2 } + 11 x + 18 } { x ^ { 2 } + 15 x + 54 } \div \frac { x ^ { 2 } + 2 x } { x ^ { 2 } + 14 x + 48 }$$
A) $\frac { x + 8 } { x ^ { 2 } + 6 x }$

B) $\frac { x } { x ^ { 2 } + 15 x + 54 }$

C) $x + 8$

D) $\frac { x + 8 } { x }$

Quizplus · Accepted Answer

To solve this division problem, first, factor all the polynomials in the numerators and denominators:$$\frac{x^2 + 11x + 18}{x^2 + 15x + 54} \div \frac{x^2 + 2x}{x^2 + 14x + 48}$$$$\frac{(x+9)(x+2)}{(x+9)(x+6)} \div \frac{x(x+2)}{(x+6)(x+8)}$$Next, remember that dividing by a fraction is the same as multiplying by its reciprocal:$$\frac{(x+9)(x+2)}{(x+9)(x+6)} \times \frac{(x+6)(x+8)}{x(x+2)}$$Cancel out the common terms:$$\frac{(x+8)}{x}$$Thus, the correct answer is D) $\frac{x + 8}{x}$.

Divide - x2+11x+18x2+15x+54÷x2+2xx2+14x+48\frac { x ^ { 2 } + 11 x + 18 } { x ^ { 2 } + 15 x + 54 } \div \frac { x ^ { 2 } + 2 x } { x ^ { 2 } + 14 x + 48 }x2+15x+54x2+11x+18​÷x2+14x+48x2+2x​

Divide
- $\frac { x ^ { 2 } + 11 x + 18 } { x ^ { 2 } + 15 x + 54 } \div \frac { x ^ { 2 } + 2 x } { x ^ { 2 } + 14 x + 48 }$