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$Perform the operation and express your answer as a single fraction in simplest form. (1)/(15x^(2))+(5x)/(3) Answer:$

Perform the operation and express your answer as a single fraction in simplest form. $\newline$ $\frac{1}{15 x^{2}}+\frac{5 x}{3}$ $\newline$ Answer:

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Roots of rational numbers

Full solution

Q. Perform the operation and express your answer as a single fraction in simplest form.

\newline

\frac{1}{15 x^{2}}+\frac{5 x}{3}

\newline

Answer:

Identify Common Denominator: Identify a common denominator for the two fractions. The denominators are $15x^2$ and $3$ . The least common multiple of these two denominators is $15x^2$ , which will be our common denominator.
Rewrite with Common Denominator: Rewrite each fraction with the common denominator. $\newline$ The first fraction $\frac{1}{15x^{2}}$ already has the common denominator, so it remains unchanged. $\newline$ The second fraction $\frac{5x}{3}$ needs to be multiplied by $\frac{5x}{5x}$ to have the common denominator of $15x^2$ . $\newline$ $\frac{5x}{3} \times \frac{5x}{5x} = \frac{25x^2}{15x^2}$
Add Fractions: Add the two fractions together. $\newline$ Now that both fractions have the same denominator, we can add the numerators together. $\newline$ $(\frac{1}{15x^{2}}) + (\frac{25x^2}{15x^2}) = (\frac{1 + 25x^2}{15x^2})$
Simplify Numerator: Simplify the numerator if possible. $\newline$ In this case, the numerator $1 + 25x^2$ cannot be simplified further. $\newline$ So the final answer is $(1 + 25x^2)/(15x^2)$ .

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