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Simplify. Express your answer as a single fraction in simplest form. $\newline$ $\frac{1}{4} + \frac{2}{w^2}$

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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{1}{4} + \frac{2}{w^2}

Identify LCD: $\frac{1}{4} + \frac{2}{w^2}$ $\newline$ Identify the least common denominator (LCD) to combine the fractions. $\newline$ The LCD for $4$ and $w^2$ is $4w^2$ .
Rewrite fractions: $\frac{1}{4} + \frac{2}{w^2}$ $\newline$ Rewrite each fraction with the common denominator $4w^2$ . $\newline$ $(\frac{1 \times w^2}{4 \times w^2}) + (\frac{2 \times 4}{w^2 \times 4})$ $\newline$ $=\frac{w^2}{4w^2} + \frac{8}{4w^2}$
Combine fractions: $(\frac{w^2}{4w^2}) + (\frac{8}{4w^2})$ $\newline$ Combine the fractions over the common denominator. $\newline$ $(\frac{w^2 + 8}{4w^2})$
Check for simplification: $(w^2 + 8)/(4w^2)$ $\newline$ Check if the numerator and denominator have any common factors that can be simplified. $\newline$ There are no common factors to simplify in this case.

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