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Simplify. Express your answer as a single fraction in simplest form. $\newline$ $\frac{4}{q} - 8q$

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Simplify mixed rational expressions

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

\newline

\frac{4}{q} - 8q

Identify common denominator: Identify the common denominator for the fractions. $\newline$ Since $\frac{4}{q}$ is already a fraction and $-8q$ is a whole number, we need to convert $-8q$ into a fraction with the same denominator as $\frac{4}{q}$ , which is $q$ .
Convert $-8q$ to fraction: Convert $-8q$ into a fraction with the denominator $q$ . To do this, we multiply $-8q$ by $\frac{q}{q}$ (which is equal to $1$ ) to get $-8q^2/q$ .
Combine fractions: Combine the fractions. $\newline$ Now we have two fractions with the same denominator, so we can combine them: $\newline$ $(\frac{4}{q}) - (\frac{8q^2}{q})$
Subtract numerators: Subtract the numerators and keep the common denominator. $\newline$ $(4 - 8q^2)/q$
Simplify expression: Simplify the expression if possible. $\newline$ In this case, the expression $(4 - 8q^2)/q$ is already in its simplest form because the numerator and the denominator do not have any common factors other than $1$ .

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