Answer
The simplified form of the expression $\frac{5}{x}+\frac{4}{{{x}^{2}}}$is$\frac{5x+4}{{{x}^{2}}}$.
Work Step by Step
$\frac{5}{x}+\frac{4}{{{x}^{2}}}$
Solve to obtain the LCD of the denominator of the fractions that is $x$and${{x}^{2}}$.
On solving the LCD is ${{x}^{2}}$.
The rational expression is written as a fraction in such a way that the LCD is the denominator of the fraction. Consider, the individual terms of the provided rational terms;
$\begin{align}
& \frac{5}{x}=\frac{5}{x}\cdot \frac{x}{x} \\
& =\frac{5x}{{{x}^{2}}}
\end{align}$
And,
$\frac{4}{{{x}^{2}}}=\frac{4}{{{x}^{2}}}$
Since the fractions have the common denominator, add the numerators and the LCD is the denominator:
$\begin{align}
& \frac{5}{x}+\frac{4}{{{x}^{2}}}=\frac{\left( 5x \right)}{{{x}^{2}}}+\frac{\left( 4 \right)}{{{x}^{2}}} \\
& =\frac{5x+4}{{{x}^{2}}}
\end{align}$
