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Simplify. Express your answer as a single fraction in simplest form. $\newline$ $\frac{2}{r^3} + \frac{2}{r}$

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Add and subtract rational expressions

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Q. Simplify. Express your answer as a single fraction in simplest form.

\newline

\frac{2}{r^3} + \frac{2}{r}

Rewrite fractions with common denominator: $\frac{2}{r^3} + \frac{2}{r}$ $\newline$ Rewrite both terms as fractions over a common denominator. $\newline$ The least common multiple of $r^3$ and $r$ is $r^3$ . So we need to express $\frac{2}{r}$ in terms of $r^3$ . $\newline$ $\frac{2}{r^3} + \frac{2}{r} = \frac{2}{r^3} + \frac{2 \cdot r^2}{r \cdot r^2}$ $\newline$ $\frac{2}{r^3} + \frac{2}{r} = \frac{2}{r^3} + \frac{2r^2}{r^3}$
Combine fractions: $\frac{2}{r^3} + \frac{2r^2}{r^3}$ $\newline$ Combine the fractions over the common denominator. $\newline$ $\frac{2 + 2r^2}{r^3}$
Simplify numerator: $(2 + 2r^2)/r^3$ $\newline$ Simplify the numerator by factoring out the common factor of $2$ . $\newline$ $2(1 + r^2)/r^3$
Final simplified expression: $2(1 + r^2)/r^3$ $\newline$ The expression is now simplified and expressed as a single fraction in simplest form.

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