Simplify.
-$$\frac { 6 + \frac { 5 } { x } } { 36 x - \frac { 25 } { x } }$$
A) $\frac { 1 } { 6 x + 5 }$
B) $6 x - 5$
C) $\frac { 1 } { 6 x - 5 }$
D) $6 x + 5$

Question

Quizplus · Accepted Answer

To simplify the given expression, factor out common terms in both the numerator and the denominator. The numerator can be rewritten as $\frac{6x}{x} + \frac{5}{x}$ which simplifies to $\frac{6x + 5}{x}$. The denominator can be rewritten as $36x - \frac{25}{x}$ which simplifies to $\frac{36x^2 - 25}{x}$. Thus, the entire expression simplifies to $\frac{\frac{6x + 5}{x}}{\frac{36x^2 - 25}{x}}$. When you divide fractions, you multiply by the reciprocal of the denominator, resulting in $\frac{6x + 5}{x} \cdot \frac{x}{36x^2 - 25}$. The $x$ in the numerator and denominator cancels out, leaving $\frac{6x + 5}{36x^2 - 25}$. Factoring the denominator as a difference of squares gives $\frac{6x + 5}{(6x + 5)(6x - 5)}$, which simplifies to $\frac{1}{6x - 5}$, making option C correct.

Simplify - 6+5x36x−25x\frac { 6 + \frac { 5 } { x } } { 36 x - \frac { 25 } { x } }36x−x25​6+x5​​

Simplify
- $\frac { 6 + \frac { 5 } { x } } { 36 x - \frac { 25 } { x } }$