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Simplify. Express your answer as a single fraction in simplest form. $\newline$ $\frac{d}{3} + \frac{1}{10d^2}$

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Add and subtract rational expressions

Full solution

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

\newline

\frac{d}{3} + \frac{1}{10d^2}

Identify LCD: Identify the least common denominator (LCD) for the fractions. $\newline$ The LCD for the fractions $\frac{d}{3}$ and $\frac{1}{10d^2}$ is $30d^2$ because $30d^2$ is the smallest number that both denominators ( $3$ and $10d^2$ ) can divide into without leaving a remainder.
Rewrite fractions: Rewrite each fraction with the common denominator. $\newline$ To rewrite $\frac{d}{3}$ with the common denominator, multiply both the numerator and the denominator by $10d^2$ . To rewrite $\frac{1}{10d^2}$ with the common denominator, multiply both the numerator and the denominator by $3$ . $\newline$ $\left(\frac{d}{3}\right) \times \left(\frac{10d^2}{10d^2}\right) + \left(\frac{1}{10d^2}\right) \times \left(\frac{3}{3}\right)$ $\newline$ = $\frac{10d^3}{30d^2}$ + $\frac{3}{30d^2}$
Combine fractions: Combine the fractions. $\newline$ Now that both fractions have the same denominator, you can combine them by adding their numerators. $\newline$ $(10d^3 + 3) / 30d^2$
Simplify expression: Simplify the expression, if possible. $\newline$ In this case, the numerator and the denominator do not have any common factors other than $1$ , so the expression is already in its simplest form. $\newline$ $(10d^3 + 3) / 30d^2$

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