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Simplify. Express your answer as a single fraction in simplest form. $\newline$ $\frac{5}{4} - \frac{p^3q}{2}$

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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{5}{4} - \frac{p^3q}{2}

Identify Common Denominator: Identify the common denominator for the fractions $\frac{5}{4}$ and $\frac{p^3q}{2}$ . The common denominator for $4$ and $2$ is $4$ , since $4$ is the least common multiple of $4$ and $2$ .
Rewrite Fractions: Rewrite the fractions with the common denominator. $\newline$ The first fraction is already over $4$ , so it remains unchanged. The second fraction needs to be adjusted to have a denominator of $4$ . $\newline$ $\frac{5}{4} - \left(\frac{p^3q}{2}\right) \times \left(\frac{2}{2}\right)$ $\newline$ $\frac{5}{4} - \frac{2p^3q}{4}$
Combine Fractions: Combine the fractions over the common denominator. $\newline$ Now that both fractions have the same denominator, we can combine them. $\newline$ $(5 - 2p^3q)/4$
Check Simplification: Check if the numerator can be simplified. $\newline$ The numerator $5 - 2p^3q$ does not have any common factors with the denominator $4$ , and there are no like terms to combine in the numerator. Therefore, the expression is already in its simplest form.

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