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Simplify. Express your answer as a single fraction in simplest form. $\newline$ $\frac{7u}{2} + \frac{u}{4}$

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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{7u}{2} + \frac{u}{4}

Identify LCD: Identify the least common denominator (LCD) for the fractions. $\newline$ The denominators are $2$ and $4$ . The LCD for these denominators is $4$ because $4$ is the smallest number that both denominators can divide into without a remainder.
Rewrite fractions: Rewrite each fraction with the LCD as the new denominator. $\newline$ For the first fraction, $\frac{7u}{2}$ , we need to multiply both the numerator and the denominator by $2$ to get the LCD of $4$ in the denominator. This gives us $(\frac{7u \times 2}{2 \times 2}) = \frac{14u}{4}$ . $\newline$ For the second fraction, $\frac{u}{4}$ , the denominator is already the LCD, so we do not need to change it.
Add fractions: Add the fractions with the common denominator. $\newline$ Now that both fractions have the same denominator, we can add them together. $\newline$ $(\frac{14u}{4}) + (\frac{u}{4}) = \frac{14u + u}{4}$
Combine like terms: Combine like terms in the numerator. $\newline$ In the numerator, we have $14u$ and $u$ , which are like terms and can be combined. $\newline$ $\frac{14u + u}{4} = \frac{15u}{4}$
Check for simplification: Check if the fraction can be simplified further. $\newline$ The fraction $(15u)/4$ is already in simplest form because $15$ and $4$ have no common factors other than $1$ .

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