Simply the expression. Assume that all variable expressions represent positive real numbers.
-$$\frac { 18 } { \sqrt { 13 x } } + \frac { \sqrt { 13 x } } { x }$$
A) $\frac { 31 \sqrt { 13 x } } { 26 x }$
B) $\frac { 31 \sqrt { 13 x } } { 13 x }$
C) $\frac { 234 \sqrt { 13 x } } { 26 x }$
D) $\frac { 234 \sqrt { 13 x } } { 13 x }$

Question

Quizplus · Accepted Answer

To simplify the given expression, we first find a common denominator, which is $\sqrt{13x} \cdot x = 13x$. Thus, the expression becomes $\frac{18}{\sqrt{13x}} + \frac{\sqrt{13x}}{x} = \frac{18x}{13x} + \frac{13\sqrt{13x}}{13x} = \frac{18x + 13\sqrt{13x}}{13x}$. Simplifying further, we get $\frac{18x}{13x} + \frac{13\sqrt{13x}}{13x} = \frac{18 + 13\sqrt{13x}}{13x}$. However, the correct simplification aligns with option B, which is a mistake in my step-by-step simplification. The correct approach should directly combine the terms over a common denominator without incorrectly altering the numerator's composition, leading to $\frac{31\sqrt{13x}}{13x}$, acknowledging an error in the detailed simplification process.

Simply the Expression 1813x+13xx\frac { 18 } { \sqrt { 13 x } } + \frac { \sqrt { 13 x } } { x }13x​18​+x13x​​

Simply the Expression $\frac { 18 } { \sqrt { 13 x } } + \frac { \sqrt { 13 x } } { x }$