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Simplify. Express your answer as a single fraction in simplest form. $\newline$ $\frac{5}{2} - \frac{bc}{5}$

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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{5}{2} - \frac{bc}{5}

Identify Common Denominator: Identify the common denominator for the fractions $\frac{5}{2}$ and $\frac{bc}{5}$ . To combine these fractions, we need a common denominator. The least common denominator (LCD) for $2$ and $5$ is $10$ .
Rewrite with Common Denominator: Rewrite each fraction with the common denominator of $10$ . For the first fraction, $\frac{5}{2}$ , we multiply the numerator and denominator by $5$ to get $\left(\frac{5\times 5}{2\times 5}\right) = \frac{25}{10}$ . For the second fraction, $\frac{bc}{5}$ , we multiply the numerator and denominator by $2$ to get $\left(\frac{bc\times 2}{5\times 2}\right) = \frac{2bc}{10}$ .
Subtract Fractions: Subtract the second fraction from the first fraction using the common denominator. $\newline$ Now we have $(\frac{25}{10}) - (\frac{2bc}{10})$ . Since the denominators are the same, we can subtract the numerators directly. $\newline$ $\frac{25}{10} - \frac{2bc}{10} = \frac{25 - 2bc}{10}$
Simplify Expression: Simplify the expression, if possible. $\newline$ The expression $(25 - 2bc)/10$ is already in its simplest form because $25$ and $2bc$ do not have any common factors other than $1$ , and the denominator cannot be reduced further.

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