Simplify.
-$$\frac { x + 6 + \frac { 9 } { x } } { x + 8 + \frac { 15 } { x } }$$
A) $\frac { ( x + 3 ) ^ { 2 } } { x + 5 }$
B) $\frac { x ^ { 2 } + 6 x + 9 } { x ^ { 2 } + 8 x + 15 }$
C) $\frac { x + 3 } { x + 5 }$
D) $\frac { x + 3 } { x ^ { 2 } + 5 x }$

Question

Quizplus · Accepted Answer

To simplify the given expression, we first find a common denominator for the fractions in the numerator and the denominator, which is $x$. The expression becomes $\frac{x^2 + 6x + 9}{x^2 + 8x + 15}$. Factoring the numerator and the denominator, we get $\frac{(x+3)^2}{(x+3)(x+5)}$. Simplifying this, we cancel out $x+3$ from the numerator and the denominator, resulting in $\frac{x+3}{x+5}$, which matches option C.

Simplify - x+6+9xx+8+15x\frac { x + 6 + \frac { 9 } { x } } { x + 8 + \frac { 15 } { x } }x+8+x15​x+6+x9​​

Simplify
- $\frac { x + 6 + \frac { 9 } { x } } { x + 8 + \frac { 15 } { x } }$