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$Perform the operation and express your answer as a single fraction in simplest form. (1)/(y^(2))+(1)/(y) Answer:$

Perform the operation and express your answer as a single fraction in simplest form. $\newline$ $\frac{1}{y^{2}}+\frac{1}{y}$ $\newline$ Answer:

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Multiplication with rational exponents

Full solution

Q. Perform the operation and express your answer as a single fraction in simplest form.

\newline

\frac{1}{y^{2}}+\frac{1}{y}

\newline

Answer:

Find Common Denominator: Identify a common denominator for the fractions. $\newline$ The fractions $\frac{1}{y^2}$ and $\frac{1}{y}$ have different denominators. To add them, we need to find a common denominator. The least common denominator (LCD) for $y^2$ and $y$ is $y^2$ .
Rewrite Fractions: Rewrite each fraction with the common denominator. $\newline$ We need to express each fraction with the denominator $y^2$ . The first fraction is already in this form, but the second fraction needs to be adjusted. $\newline$ rac{1}{y^2} stays the same, and rac{1}{y} needs to be multiplied by rac{y}{y} to have the common denominator $y^2$ . $\newline$ So, rac{1}{y} becomes rac{y}{y^2}.
Add Fractions: Add the fractions. $\newline$ Now that both fractions have the same denominator, we can add them together. $\newline$ $(\frac{1}{y^2}) + (\frac{y}{y^2}) = \frac{1 + y}{y^2}$
Simplify Result: Simplify the numerator if possible. $\newline$ The numerator $1 + y$ is already in its simplest form, so the fraction $\frac{1 + y}{y^2}$ is the final answer.

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