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Simplify. Express your answer as a single fraction in simplest form. $\newline$ $\frac{qr}{5} + \frac{q^5r^4}{4}$

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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{qr}{5} + \frac{q^5r^4}{4}

Identify Common Denominator: Identify the common denominator for the fractions $\frac{qr}{5}$ and $\frac{q^5r^4}{4}$ . Since the denominators are $5$ and $4$ , the least common denominator (LCD) is their least common multiple, which is $20$ .
Rewrite with Common Denominator: Rewrite each fraction with the common denominator of $20$ . For the first fraction, multiply both the numerator and the denominator by $4$ to get $(4qr)/20$ . For the second fraction, multiply both the numerator and the denominator by $5$ to get $(5q^5r^4)/20$ .
Combine Fractions: Combine the fractions over the common denominator. $\newline$ Now that both fractions have the same denominator, we can combine them: $\newline$ $(4qr)/20 + (5q^5r^4)/20 = (4qr + 5q^5r^4)/20$
Simplify Expression: Simplify the expression if possible. $\newline$ In this case, there are no common factors in the numerator that can be canceled with the denominator, so the expression is already in its simplest form.

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