## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson

# Chapter R - Elementary Algebra Review - R.6 Rational Expressions and Equations - R.6 Exercise Set - Page 980: 17

#### 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}

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