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Simplify. Express your answer as a single fraction in simplest form. $\newline$ $\frac{6u}{5} + 6u$

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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{6u}{5} + 6u

Identify Common Denominator: Identify the common denominator for the fractions. $\newline$ Since $6u$ is not a fraction, we can rewrite it as a fraction with a denominator of $1$ to find a common denominator with $\frac{6u}{5}$ .
Rewrite $6u$ as Fraction: Rewrite $6u$ as a fraction. $\newline$ $6u = \frac{6u}{1}$ $\newline$ Now we have two fractions: $\frac{6u}{5}$ and $\frac{6u}{1}$ .
Find Common Denominator: Find a common denominator for the two fractions. $\newline$ The common denominator for $5$ and $1$ is $5$ . So we will rewrite $\frac{6u}{1}$ with the common denominator of $5$ . $\newline$ $\frac{6u}{1} = \frac{6u \times 5}{1 \times 5} = \frac{30u}{5}$
Rewrite with Common Denominator: Rewrite the original expression with the common denominator. $\frac{6u}{5} + 6u = \frac{6u}{5} + \frac{30u}{5}$
Combine Fractions: Combine the fractions. $\newline$ Now that we have a common denominator, we can combine the numerators. $\newline$ $(6u + 30u)/5 = 36u/5$
Simplify Fraction: Simplify the fraction, if possible. $\newline$ In this case, the fraction $\frac{36u}{5}$ is already in simplest form because $36$ and $5$ have no common factors other than $1$ .

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