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Simplify. Express your answer as a single fraction in simplest form. $\newline$ $\frac{pq}{2} - \frac{p}{4}$

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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{pq}{2} - \frac{p}{4}

Identify LCD: Identify the least common denominator (LCD) for the fractions $\frac{pq}{2}$ and $\frac{p}{4}$ . The LCD for $2$ and $4$ is $4$ because $4$ is the smallest number that both denominators divide into evenly.
Rewrite fractions: Rewrite each fraction with the LCD as the denominator. $\newline$ For $\frac{pq}{2}$ , multiply both the numerator and the denominator by $2$ to get $\frac{2pq}{4}$ . $\newline$ For $\frac{p}{4}$ , the denominator is already $4$ , so it remains $\frac{p}{4}$ .
Combine fractions: Combine the fractions with the common denominator. (\(2pq)/ $4$ - p/ $4$ = ( $2$ pq - p)/ $4$
Simplify numerator: Simplify the numerator if possible. $\newline$ In the numerator $2pq - p$ , factor out the common factor $p$ . $\newline$ $p(2q - 1)$
Write final expression: Write the simplified numerator over the common denominator. $\newline$ The final simplified expression is $\frac{p(2q - 1)}{4}.$

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